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La ecuación:
Ecuación (7-x)^2=(x+16)^2
Ecuación 11x-9=4x+19
Ecuación 10x+9=7x
Ecuación x-x/7=15/7
Expresar {x} en función de y en la ecuación:
4*x+15*y=19
7*x-2*y=20
-8*x-12*y=15
1*x+7*y=8
Expresiones idénticas
- dieciséis *(x^ tres)-(veinticinco . cuarenta y seis *x)- veinte mil setecientos setenta y cinco . tres = cero
menos 16 multiplicar por (x al cubo ) menos (25.46 multiplicar por x) menos 20775.3 es igual a 0
menos dieciséis multiplicar por (x en el grado tres) menos (veinticinco . cuarenta y seis multiplicar por x) menos veinte mil setecientos setenta y cinco . tres es igual a cero
-16*(x3)-(25.46*x)-20775.3=0
-16*x3-25.46*x-20775.3=0
-16*(x³)-(25.46*x)-20775.3=0
-16*(x en el grado 3)-(25.46*x)-20775.3=0
-16(x^3)-(25.46x)-20775.3=0
-16(x3)-(25.46x)-20775.3=0
-16x3-25.46x-20775.3=0
-16x^3-25.46x-20775.3=0
-16*(x^3)-(25.46*x)-20775.3=O
Expresiones semejantes
-16*(x^3)-(25.46*x)+20775.3=0
16*(x^3)-(25.46*x)-20775.3=0
-16*(x^3)+(25.46*x)-20775.3=0

-16(x^3)-(25.46x)-20775.3=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

      3   1273*x   207753    
- 16*x  - ------ - ------ = 0
            50       10

\left(- 16 x^{3} - \frac{1273 x}{50}\right) - \frac{207753}{10} = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(- 16 x^{3} - \frac{1273 x}{50}\right) - \frac{207753}{10} = 0

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} + \frac{1273 x}{800} + \frac{207753}{160} = 0

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = 0

q = \frac{c}{a}

q = \frac{1273}{800}

v = \frac{d}{a}

v = \frac{207753}{160}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = 0

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{1273}{800}

x_{1} x_{2} x_{3} = \frac{207753}{160}

Respuesta rápida [src]

                                                            ___________________________________     /           ___________________________________                                                \
                                                           /               ___________________      |          /               ___________________                                                 |
                                                          /  5609331   3*\/ 34960672674890502       |  ___    /  5609331   3*\/ 34960672674890502                                                  |
                                                       3 /   ------- + -----------------------      |\/ 3 *3 /   ------- + -----------------------                             ___                 |
                            1273                       \/      320              32000               |      \/      320              32000                               1273*\/ 3                  |
x1 = - --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------|
                 ___________________________________                      6                         |                      6                                    ___________________________________|
                /               ___________________                                                 |                                                          /               ___________________ |
               /  5609331   3*\/ 34960672674890502                                                  |                                                         /  5609331   3*\/ 34960672674890502  |
       1600*3 /   ------- + -----------------------                                                 |                                                 1600*3 /   ------- + ----------------------- |
            \/      320              32000                                                          \                                                      \/      320              32000          /

x_{1} = - \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)

                                                            ___________________________________     /                                                             ___________________________________\
                                                           /               ___________________      |                                                            /               ___________________ |
                                                          /  5609331   3*\/ 34960672674890502       |                                                    ___    /  5609331   3*\/ 34960672674890502  |
                                                       3 /   ------- + -----------------------      |                           ___                    \/ 3 *3 /   ------- + ----------------------- |
                            1273                       \/      320              32000               |                    1273*\/ 3                           \/      320              32000          |
x2 = - --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------|
                 ___________________________________                      6                         |            ___________________________________                         6                       |
                /               ___________________                                                 |           /               ___________________                                                  |
               /  5609331   3*\/ 34960672674890502                                                  |          /  5609331   3*\/ 34960672674890502                                                   |
       1600*3 /   ------- + -----------------------                                                 |  1600*3 /   ------- + -----------------------                                                  |
            \/      320              32000                                                          \       \/      320              32000                                                           /

x_{2} = - \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)

            ___________________________________                                               
           /               ___________________                                                
          /  5609331   3*\/ 34960672674890502                                                 
       3 /   ------- + -----------------------                                                
       \/      320              32000                                 1273                    
x3 = - ---------------------------------------- + --------------------------------------------
                          3                                ___________________________________
                                                          /               ___________________ 
                                                         /  5609331   3*\/ 34960672674890502  
                                                  800*3 /   ------- + ----------------------- 
                                                      \/      320              32000

x_{3} = - \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}

x3 = -(5609331/320 + 3*sqrt(34960672674890502)/32000)^(1/3)/3 + 1273/(800*(5609331/320 + 3*sqrt(34960672674890502)/32000)^(1/3))

Suma y producto de raíces [src]

suma

                                                       ___________________________________     /           ___________________________________                                                \                                                          ___________________________________     /                                                             ___________________________________\          ___________________________________                                               
                                                      /               ___________________      |          /               ___________________                                                 |                                                         /               ___________________      |                                                            /               ___________________ |         /               ___________________                                                
                                                     /  5609331   3*\/ 34960672674890502       |  ___    /  5609331   3*\/ 34960672674890502                                                  |                                                        /  5609331   3*\/ 34960672674890502       |                                                    ___    /  5609331   3*\/ 34960672674890502  |        /  5609331   3*\/ 34960672674890502                                                 
                                                  3 /   ------- + -----------------------      |\/ 3 *3 /   ------- + -----------------------                             ___                 |                                                     3 /   ------- + -----------------------      |                           ___                    \/ 3 *3 /   ------- + ----------------------- |     3 /   ------- + -----------------------                                                
                       1273                       \/      320              32000               |      \/      320              32000                               1273*\/ 3                  |                          1273                       \/      320              32000               |                    1273*\/ 3                           \/      320              32000          |     \/      320              32000                                 1273                    
- --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------| + - --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------| + - ---------------------------------------- + --------------------------------------------
            ___________________________________                      6                         |                      6                                    ___________________________________|               ___________________________________                      6                         |            ___________________________________                         6                       |                        3                                ___________________________________
           /               ___________________                                                 |                                                          /               ___________________ |              /               ___________________                                                 |           /               ___________________                                                  |                                                        /               ___________________ 
          /  5609331   3*\/ 34960672674890502                                                  |                                                         /  5609331   3*\/ 34960672674890502  |             /  5609331   3*\/ 34960672674890502                                                  |          /  5609331   3*\/ 34960672674890502                                                   |                                                       /  5609331   3*\/ 34960672674890502  
  1600*3 /   ------- + -----------------------                                                 |                                                 1600*3 /   ------- + ----------------------- |     1600*3 /   ------- + -----------------------                                                 |  1600*3 /   ------- + -----------------------                                                  |                                                800*3 /   ------- + ----------------------- 
       \/      320              32000                                                          \                                                      \/      320              32000          /          \/      320              32000                                                          \       \/      320              32000                                                           /                                                    \/      320              32000

\left(- \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right) + \left(\left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)\right) + \left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)\right)\right)

  /                                                             ___________________________________\     /           ___________________________________                                                \
  |                                                            /               ___________________ |     |          /               ___________________                                                 |
  |                                                    ___    /  5609331   3*\/ 34960672674890502  |     |  ___    /  5609331   3*\/ 34960672674890502                                                  |
  |                           ___                    \/ 3 *3 /   ------- + ----------------------- |     |\/ 3 *3 /   ------- + -----------------------                             ___                 |
  |                    1273*\/ 3                           \/      320              32000          |     |      \/      320              32000                               1273*\/ 3                  |
I*|- --------------------------------------------- - ----------------------------------------------| + I*|---------------------------------------------- + ---------------------------------------------|
  |            ___________________________________                         6                       |     |                      6                                    ___________________________________|
  |           /               ___________________                                                  |     |                                                          /               ___________________ |
  |          /  5609331   3*\/ 34960672674890502                                                   |     |                                                         /  5609331   3*\/ 34960672674890502  |
  |  1600*3 /   ------- + -----------------------                                                  |     |                                                 1600*3 /   ------- + ----------------------- |
  \       \/      320              32000                                                           /     \                                                      \/      320              32000          /

i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right) + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)

producto

/                                                       ___________________________________     /           ___________________________________                                                \\ /                                                       ___________________________________     /                                                             ___________________________________\\ /       ___________________________________                                               \
|                                                      /               ___________________      |          /               ___________________                                                 || |                                                      /               ___________________      |                                                            /               ___________________ || |      /               ___________________                                                |
|                                                     /  5609331   3*\/ 34960672674890502       |  ___    /  5609331   3*\/ 34960672674890502                                                  || |                                                     /  5609331   3*\/ 34960672674890502       |                                                    ___    /  5609331   3*\/ 34960672674890502  || |     /  5609331   3*\/ 34960672674890502                                                 |
|                                                  3 /   ------- + -----------------------      |\/ 3 *3 /   ------- + -----------------------                             ___                 || |                                                  3 /   ------- + -----------------------      |                           ___                    \/ 3 *3 /   ------- + ----------------------- || |  3 /   ------- + -----------------------                                                |
|                       1273                       \/      320              32000               |      \/      320              32000                               1273*\/ 3                  || |                       1273                       \/      320              32000               |                    1273*\/ 3                           \/      320              32000          || |  \/      320              32000                                 1273                    |
|- --------------------------------------------- + ---------------------------------------- + I*|---------------------------------------------- + ---------------------------------------------||*|- --------------------------------------------- + ---------------------------------------- + I*|- --------------------------------------------- - ----------------------------------------------||*|- ---------------------------------------- + --------------------------------------------|
|            ___________________________________                      6                         |                      6                                    ___________________________________|| |            ___________________________________                      6                         |            ___________________________________                         6                       || |                     3                                ___________________________________|
|           /               ___________________                                                 |                                                          /               ___________________ || |           /               ___________________                                                 |           /               ___________________                                                  || |                                                     /               ___________________ |
|          /  5609331   3*\/ 34960672674890502                                                  |                                                         /  5609331   3*\/ 34960672674890502  || |          /  5609331   3*\/ 34960672674890502                                                  |          /  5609331   3*\/ 34960672674890502                                                   || |                                                    /  5609331   3*\/ 34960672674890502  |
|  1600*3 /   ------- + -----------------------                                                 |                                                 1600*3 /   ------- + ----------------------- || |  1600*3 /   ------- + -----------------------                                                 |  1600*3 /   ------- + -----------------------                                                  || |                                             800*3 /   ------- + ----------------------- |
\       \/      320              32000                                                          \                                                      \/      320              32000          // \       \/      320              32000                                                          \       \/      320              32000                                                           // \                                                 \/      320              32000          /

\left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(\frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6}\right)\right) \left(- \frac{1273}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}} + \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{6} - \frac{1273 \sqrt{3}}{1600 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}{3} + \frac{1273}{800 \sqrt[3]{\frac{5609331}{320} + \frac{3 \sqrt{34960672674890502}}{32000}}}\right)

-207753 
--------
  160

- \frac{207753}{160}

-207753/160

Respuesta numérica [src]

x1 = 5.43049405917003 - 9.49010259059632*i

x2 = -10.8609881183401

x3 = 5.43049405917003 + 9.49010259059632*i

x3 = 5.43049405917003 + 9.49010259059632*i

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-16*(x^3)-(25.46*x)-20775.3=0 la ecuación

Solución numérica:

Solución

-16(x^3)-(25.46x)-20775.3=0 la ecuación