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La ecuación:
Ecuación 4^x-3*2^x+2=0
Ecuación (x-2)/(x-7)=5/8
Ecuación 4/(x-4)=-5
Ecuación (x-6)^2=-24*x
Expresar {x} en función de y en la ecuación:
20*x+5*y=-3
-11*x-14*y=-3
20*x+18*y=-9
-2*x+2*y=4
Expresiones idénticas
(sqrt(x+ cuatro)+sqrt(x+ cuatro))/ dos =x+sqrt(x^(dos)- dieciséis)- seis
( raíz cuadrada de (x más 4) más raíz cuadrada de (x más 4)) dividir por 2 es igual a x más raíz cuadrada de (x en el grado (2) menos 16) menos 6
( raíz cuadrada de (x más cuatro) más raíz cuadrada de (x más cuatro)) dividir por dos es igual a x más raíz cuadrada de (x en el grado (dos) menos dieciséis) menos seis
(√(x+4)+√(x+4))/2=x+√(x^(2)-16)-6
(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x(2)-16)-6
sqrtx+4+sqrtx+4/2=x+sqrtx2-16-6
sqrtx+4+sqrtx+4/2=x+sqrtx^2-16-6
(sqrt(x+4)+sqrt(x+4)) dividir por 2=x+sqrt(x^(2)-16)-6
Expresiones semejantes
(sqrt(x+4)-sqrt(x+4))/2=x+sqrt(x^(2)-16)-6
(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)+16)-6
(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)+6
(sqrt(x+4)+sqrt(x+4))/2=x-sqrt(x^(2)-16)-6
(sqrt(x-4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)-6
(sqrt(x+4)+sqrt(x-4))/2=x+sqrt(x^(2)-16)-6
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x)=1
sqrt(12+x)-sqrt(1-x)=1
sqrt(12-x)=x
sqrt(x-2)+sqrt(y-2)=2
sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)
Raíz cuadrada sqrt
sqrt(x)=1
sqrt(12+x)-sqrt(1-x)=1
sqrt(12-x)=x
sqrt(x-2)+sqrt(y-2)=2
sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)
Raíz cuadrada sqrt
sqrt(x)=1
sqrt(12+x)-sqrt(1-x)=1
sqrt(12-x)=x
sqrt(x-2)+sqrt(y-2)=2
sqrt(2-x)+sqrt(-x-1)=sqrt(-5*x-7)

(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)-6 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

  _______     _______          _________    
\/ x + 4  + \/ x + 4          /  2          
--------------------- = x + \/  x  - 16  - 6
          2

\frac{\sqrt{x + 4} + \sqrt{x + 4}}{2} = \left(x + \sqrt{x^{2} - 16}\right) - 6

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

            /                     1                     \     /       /                     1                     \                                                                      \                                                                      
     3067*re|-------------------------------------------|     |3067*im|-------------------------------------------|               /    /       _____\\               /    /       _____\\|               /    /       _____\\               /    /       _____\\
            |                     ______________________|     |       |                     ______________________|               |    |1600*\/ 669 ||               |    |1600*\/ 669 |||               |    |1600*\/ 669 ||               |    |1600*\/ 669 ||
            |/          ___\     /                _____ |     |       |/          ___\     /                _____ |               |atan|------------||               |atan|------------|||               |atan|------------||               |atan|------------||
            ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     |       ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     ______    |    \   291267   /|     ______    |    \   291267   /||     ______    |    \   291267   /|     ______    |    \   291267   /|
            ||- - - -------|*3 /   ----- + ------------ |     |       ||- - - -------|*3 /   ----- + ------------ |   \/ 3067 *cos|------------------|   \/ 9201 *sin|------------------||   \/ 9201 *cos|------------------|   \/ 3067 *sin|------------------|
51          \\  2      2   / \/      64         9       /     |       \\  2      2   / \/      64         9       /               \        3         /               \        3         /|               \        3         /               \        3         /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4                             48                              \                         48                                           8                                  24               /                  24                                 8

- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)

            /                     1                     \     /       /                     1                     \                                                                      \                                                                      
     3067*re|-------------------------------------------|     |3067*im|-------------------------------------------|               /    /       _____\\               /    /       _____\\|               /    /       _____\\               /    /       _____\\
            |                     ______________________|     |       |                     ______________________|               |    |1600*\/ 669 ||               |    |1600*\/ 669 |||               |    |1600*\/ 669 ||               |    |1600*\/ 669 ||
            |/          ___\     /                _____ |     |       |/          ___\     /                _____ |               |atan|------------||               |atan|------------|||               |atan|------------||               |atan|------------||
            ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     |       ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     ______    |    \   291267   /|     ______    |    \   291267   /||     ______    |    \   291267   /|     ______    |    \   291267   /|
            ||- - - -------|*3 /   ----- + ------------ |     |       ||- - - -------|*3 /   ----- + ------------ |   \/ 3067 *cos|------------------|   \/ 9201 *sin|------------------||   \/ 9201 *cos|------------------|   \/ 3067 *sin|------------------|
51          \\  2      2   / \/      64         9       /     |       \\  2      2   / \/      64         9       /               \        3         /               \        3         /|               \        3         /               \        3         /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4                             48                              \                         48                                           8                                  24               /                  24                                 8

- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)

producto

            /                     1                     \     /       /                     1                     \                                                                      \                                                                      
     3067*re|-------------------------------------------|     |3067*im|-------------------------------------------|               /    /       _____\\               /    /       _____\\|               /    /       _____\\               /    /       _____\\
            |                     ______________________|     |       |                     ______________________|               |    |1600*\/ 669 ||               |    |1600*\/ 669 |||               |    |1600*\/ 669 ||               |    |1600*\/ 669 ||
            |/          ___\     /                _____ |     |       |/          ___\     /                _____ |               |atan|------------||               |atan|------------|||               |atan|------------||               |atan|------------||
            ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     |       ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     ______    |    \   291267   /|     ______    |    \   291267   /||     ______    |    \   291267   /|     ______    |    \   291267   /|
            ||- - - -------|*3 /   ----- + ------------ |     |       ||- - - -------|*3 /   ----- + ------------ |   \/ 3067 *cos|------------------|   \/ 9201 *sin|------------------||   \/ 9201 *cos|------------------|   \/ 3067 *sin|------------------|
51          \\  2      2   / \/      64         9       /     |       \\  2      2   / \/      64         9       /               \        3         /               \        3         /|               \        3         /               \        3         /
-- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
4                             48                              \                         48                                           8                                  24               /                  24                                 8

- \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)

                 /      /       _____\     \
                 |      |1600*\/ 669 |     |
                 |  atan|------------|     |
       ______    |      \   291267   /   pi|
     \/ 9201 *sin|- ------------------ + --|
51               \          3            6 /
-- - ---------------------------------------
4                       6

- \frac{\sqrt{9201} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} + \frac{\pi}{6} \right)}}{6} + \frac{51}{4}

51/4 - sqrt(9201)*sin(-atan(1600*sqrt(669)/291267)/3 + pi/6)/6

Respuesta rápida [src]

                 /                     1                     \     /       /                     1                     \                                                                      \                                                                      
          3067*re|-------------------------------------------|     |3067*im|-------------------------------------------|               /    /       _____\\               /    /       _____\\|               /    /       _____\\               /    /       _____\\
                 |                     ______________________|     |       |                     ______________________|               |    |1600*\/ 669 ||               |    |1600*\/ 669 |||               |    |1600*\/ 669 ||               |    |1600*\/ 669 ||
                 |/          ___\     /                _____ |     |       |/          ___\     /                _____ |               |atan|------------||               |atan|------------|||               |atan|------------||               |atan|------------||
                 ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     |       ||  1   I*\/ 3 |    /  32363   25*I*\/ 669  |     ______    |    \   291267   /|     ______    |    \   291267   /||     ______    |    \   291267   /|     ______    |    \   291267   /|
                 ||- - - -------|*3 /   ----- + ------------ |     |       ||- - - -------|*3 /   ----- + ------------ |   \/ 3067 *cos|------------------|   \/ 9201 *sin|------------------||   \/ 9201 *cos|------------------|   \/ 3067 *sin|------------------|
     51          \\  2      2   / \/      64         9       /     |       \\  2      2   / \/      64         9       /               \        3         /               \        3         /|               \        3         /               \        3         /
x1 = -- + ---------------------------------------------------- + I*|---------------------------------------------------- - -------------------------------- - --------------------------------| - -------------------------------- + --------------------------------
     4                             48                              \                         48                                           8                                  24               /                  24                                 8

x_{1} = - \frac{\sqrt{9201} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48} + \frac{\sqrt{3067} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} + \frac{51}{4} + i \left(- \frac{\sqrt{3067} \cos{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{8} - \frac{\sqrt{9201} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1600 \sqrt{669}}{291267} \right)}}{3} \right)}}{24} + \frac{3067 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{32363}{64} + \frac{25 \sqrt{669} i}{9}}}\right)}}{48}\right)

x1 = -sqrt(9201)*cos(atan(1600*sqrt(669)/291267)/3)/24 + 3067*re(1/((-1/2 - sqrt(3)*i/2)*(32363/64 + 25*sqrt(669)*i/9)^(1/3)))/48 + sqrt(3067)*sin(atan(1600*sqrt(669)/291267)/3)/8 + 51/4 + i*(-sqrt(3067)*cos(atan(1600*sqrt(669)/291267)/3)/8 - sqrt(9201)*sin(atan(1600*sqrt(669)/291267)/3)/24 + 3067*im(1/((-1/2 - sqrt(3)*i/2)*(32363/64 + 25*sqrt(669)*i/9)^(1/3)))/48)

Respuesta numérica [src]

x1 = 5.41647598981574

x1 = 5.41647598981574

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

(sqrt(x+4)+sqrt(x+4))/2=x+sqrt(x^(2)-16)-6 la ecuación

Solución numérica:

Solución