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La ecuación:
Ecuación x^2+11=0
Ecuación x^3-x^2-x-1=0
Ecuación 5x+12=8x+30
Ecuación 1/x^2-3/x-4=0
Expresar {x} en función de y en la ecuación:
-7*x-13*y=5
15*x+1*y=19
7*x-1*y=-7
20*x+5*y=-3
Expresiones idénticas
(x(x+ dos))^ dos = dieciséis (cuatro -x^ dos)
(x(x más 2)) al cuadrado es igual a 16(4 menos x al cuadrado )
(x(x más dos)) en el grado dos es igual a dieciséis (cuatro menos x en el grado dos)
(x(x+2))2=16(4-x2)
xx+22=164-x2
(x(x+2))²=16(4-x²)
(x(x+2)) en el grado 2=16(4-x en el grado 2)
xx+2^2=164-x^2
Expresiones semejantes
(x(x-2))^2=16(4-x^2)
(x(x+2))^2=16(4+x^2)

(x(x+2))^2=16(4-x^2) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

           2      /     2\
(x*(x + 2))  = 16*\4 - x /

$$\left(x \left(x + 2\right)\right)^{2} = 16 \left(4 - x^{2}\right)$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

x1 = -2

$$x_{1} = -2$$

                ________________                               /             ________________                          \
               /          _____                                |            /          _____                 ___       |
       2      /  71   2*\/ 177                11               |    ___    /  71   2*\/ 177             11*\/ 3        |
x2 = - - - 3 /   -- + ---------  + ----------------------- + I*|- \/ 3 *3 /   -- + ---------  - -----------------------|
       3   \/    27       9               ________________     |        \/    27       9               ________________|
                                         /          _____      |                                      /          _____ |
                                        /  71   2*\/ 177       |                                     /  71   2*\/ 177  |
                                   9*3 /   -- + ---------      |                                9*3 /   -- + --------- |
                                     \/    27       9          \                                  \/    27       9     /

$$x_{2} = - \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(- \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}}\right)$$

                ________________                               /           ________________                          \
               /          _____                                |          /          _____                 ___       |
       2      /  71   2*\/ 177                11               |  ___    /  71   2*\/ 177             11*\/ 3        |
x3 = - - - 3 /   -- + ---------  + ----------------------- + I*|\/ 3 *3 /   -- + ---------  + -----------------------|
       3   \/    27       9               ________________     |      \/    27       9               ________________|
                                         /          _____      |                                    /          _____ |
                                        /  71   2*\/ 177       |                                   /  71   2*\/ 177  |
                                   9*3 /   -- + ---------      |                              9*3 /   -- + --------- |
                                     \/    27       9          \                                \/    27       9     /

$$x_{3} = - \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(\frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right)$$

                  ________________                          
                 /          _____                           
       2        /  71   2*\/ 177                22          
x4 = - - + 2*3 /   -- + ---------  - -----------------------
       3     \/    27       9               ________________
                                           /          _____ 
                                          /  71   2*\/ 177  
                                     9*3 /   -- + --------- 
                                       \/    27       9

$$x_{4} = - \frac{22}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} - \frac{2}{3} + 2 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}$$

x4 = -22/(9*(71/27 + 2*sqrt(177)/9)^(1/3)) - 2/3 + 2*(71/27 + 2*sqrt(177)/9)^(1/3)

Suma y producto de raíces [src]

suma

                ________________                               /             ________________                          \              ________________                               /           ________________                          \                ________________                          
               /          _____                                |            /          _____                 ___       |             /          _____                                |          /          _____                 ___       |               /          _____                           
       2      /  71   2*\/ 177                11               |    ___    /  71   2*\/ 177             11*\/ 3        |     2      /  71   2*\/ 177                11               |  ___    /  71   2*\/ 177             11*\/ 3        |     2        /  71   2*\/ 177                22          
-2 + - - - 3 /   -- + ---------  + ----------------------- + I*|- \/ 3 *3 /   -- + ---------  - -----------------------| + - - - 3 /   -- + ---------  + ----------------------- + I*|\/ 3 *3 /   -- + ---------  + -----------------------| + - - + 2*3 /   -- + ---------  - -----------------------
       3   \/    27       9               ________________     |        \/    27       9               ________________|     3   \/    27       9               ________________     |      \/    27       9               ________________|     3     \/    27       9               ________________
                                         /          _____      |                                      /          _____ |                                       /          _____      |                                    /          _____ |                                         /          _____ 
                                        /  71   2*\/ 177       |                                     /  71   2*\/ 177  |                                      /  71   2*\/ 177       |                                   /  71   2*\/ 177  |                                        /  71   2*\/ 177  
                                   9*3 /   -- + ---------      |                                9*3 /   -- + --------- |                                 9*3 /   -- + ---------      |                              9*3 /   -- + --------- |                                   9*3 /   -- + --------- 
                                     \/    27       9          \                                  \/    27       9     /                                   \/    27       9          \                                \/    27       9     /                                     \/    27       9

$$\left(- \frac{22}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} - \frac{2}{3} + 2 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right) + \left(\left(-2 + \left(- \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(- \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}}\right)\right)\right) + \left(- \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(\frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right)\right)\right)$$

       /           ________________                          \     /             ________________                          \
       |          /          _____                 ___       |     |            /          _____                 ___       |
       |  ___    /  71   2*\/ 177             11*\/ 3        |     |    ___    /  71   2*\/ 177             11*\/ 3        |
-4 + I*|\/ 3 *3 /   -- + ---------  + -----------------------| + I*|- \/ 3 *3 /   -- + ---------  - -----------------------|
       |      \/    27       9               ________________|     |        \/    27       9               ________________|
       |                                    /          _____ |     |                                      /          _____ |
       |                                   /  71   2*\/ 177  |     |                                     /  71   2*\/ 177  |
       |                              9*3 /   -- + --------- |     |                                9*3 /   -- + --------- |
       \                                \/    27       9     /     \                                  \/    27       9     /

$$-4 + i \left(- \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}}\right) + i \left(\frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right)$$

producto

   /           ________________                               /             ________________                          \\ /           ________________                               /           ________________                          \\ /             ________________                          \
   |          /          _____                                |            /          _____                 ___       || |          /          _____                                |          /          _____                 ___       || |            /          _____                           |
   |  2      /  71   2*\/ 177                11               |    ___    /  71   2*\/ 177             11*\/ 3        || |  2      /  71   2*\/ 177                11               |  ___    /  71   2*\/ 177             11*\/ 3        || |  2        /  71   2*\/ 177                22          |
-2*|- - - 3 /   -- + ---------  + ----------------------- + I*|- \/ 3 *3 /   -- + ---------  - -----------------------||*|- - - 3 /   -- + ---------  + ----------------------- + I*|\/ 3 *3 /   -- + ---------  + -----------------------||*|- - + 2*3 /   -- + ---------  - -----------------------|
   |  3   \/    27       9               ________________     |        \/    27       9               ________________|| |  3   \/    27       9               ________________     |      \/    27       9               ________________|| |  3     \/    27       9               ________________|
   |                                    /          _____      |                                      /          _____ || |                                    /          _____      |                                    /          _____ || |                                      /          _____ |
   |                                   /  71   2*\/ 177       |                                     /  71   2*\/ 177  || |                                   /  71   2*\/ 177       |                                   /  71   2*\/ 177  || |                                     /  71   2*\/ 177  |
   |                              9*3 /   -- + ---------      |                                9*3 /   -- + --------- || |                              9*3 /   -- + ---------      |                              9*3 /   -- + --------- || |                                9*3 /   -- + --------- |
   \                                \/    27       9          \                                  \/    27       9     // \                                \/    27       9          \                                \/    27       9     // \                                  \/    27       9     /

$$\left(- \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(\frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right)\right) \left(- 2 \left(- \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{2}{3} + \frac{11}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} + i \left(- \sqrt{3} \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}} - \frac{11 \sqrt{3}}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}}\right)\right)\right) \left(- \frac{22}{9 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}} - \frac{2}{3} + 2 \sqrt[3]{\frac{71}{27} + \frac{2 \sqrt{177}}{9}}\right)$$

-64

$$-64$$

-64

Respuesta numérica [src]

x1 = -1.75217177888419 - 4.26633691972608*i

x2 = -1.75217177888419 + 4.26633691972608*i

x3 = 1.50434355776837

x4 = -2.0

x4 = -2.0

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Expresiones idénticas

Expresiones semejantes

(x(x+2))^2=16(4-x^2) la ecuación

Solución numérica:

Solución