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La ecuación:
Ecuación 3^x=4
Ecuación 6*x^2+x-7=0
Ecuación 15-16x+4x^2=0
Ecuación 3*x=5
Expresar {x} en función de y en la ecuación:
6*x-19*y=-18
3*x-12*y=-14
17*x-19*y=-12
-4*x+14*y=-2
Expresiones idénticas
(x^ dos + cuatro)^ dos +(x^ dos - seis *x- dieciséis)^ dos = cero
(x al cuadrado más 4) al cuadrado más (x al cuadrado menos 6 multiplicar por x menos 16) al cuadrado es igual a 0
(x en el grado dos más cuatro) en el grado dos más (x en el grado dos menos seis multiplicar por x menos dieciséis) en el grado dos es igual a cero
(x2+4)2+(x2-6*x-16)2=0
x2+42+x2-6*x-162=0
(x²+4)²+(x²-6*x-16)²=0
(x en el grado 2+4) en el grado 2+(x en el grado 2-6*x-16) en el grado 2=0
(x^2+4)^2+(x^2-6x-16)^2=0
(x2+4)2+(x2-6x-16)2=0
x2+42+x2-6x-162=0
x^2+4^2+x^2-6x-16^2=0
(x^2+4)^2+(x^2-6*x-16)^2=O
Expresiones semejantes
(x^2+4)^2+(x^2-6*x+16)^2=0
(x^2-4)^2+(x^2-6*x-16)^2=0
(x^2+4)^2-(x^2-6*x-16)^2=0
(x^2+4)^2+(x^2+6*x-16)^2=0

(x^2+4)^2+(x^2-6*x-16)^2=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

        2                  2    
/ 2    \    / 2           \     
\x  + 4/  + \x  - 6*x - 16/  = 0

\left(x^{2} + 4\right)^{2} + \left(\left(x^{2} - 6 x\right) - 16\right)^{2} = 0

Simplificar

Respuesta rápida [src]

           /                       /    /29\\\                    /    /29\\
           |                       |atan|--|||                    |atan|--||
           |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|
           |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|
     3     |  3                    \   2    /|                    \   2    /
x1 = - + I*|- - + ---------------------------| - ---------------------------
     2     \  2                2             /                2

x_{1} = - \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)

           /                     /    /29\\\                    /    /29\\
           |                     |atan|--|||                    |atan|--||
           |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|
           |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|
     3     |3                    \   2    /|                    \   2    /
x2 = - + I*|- + ---------------------------| + ---------------------------
     2     \2                2             /                2

x_{2} = \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)

           /                       /    /29\\\                    /    /29\\
           |                       |atan|--|||                    |atan|--||
           |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|
           |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|
     3     |  3                    \   2    /|                    \   2    /
x3 = - + I*|- - - ---------------------------| + ---------------------------
     2     \  2                2             /                2

x_{3} = \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} - \frac{3}{2}\right)

           /                     /    /29\\\                    /    /29\\
           |                     |atan|--|||                    |atan|--||
           |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|
           |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|
     3     |3                    \   2    /|                    \   2    /
x4 = - + I*|- - ---------------------------| - ---------------------------
     2     \2                2             /                2

x_{4} = - \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2}\right)

x4 = -sqrt(2)*985^(1/4)*cos(atan(29/12)/2)/2 + 3/2 + i*(-sqrt(2)*985^(1/4)*sin(atan(29/12)/2)/2 + 3/2)

Suma y producto de raíces [src]

suma

      /                       /    /29\\\                    /    /29\\         /                     /    /29\\\                    /    /29\\         /                       /    /29\\\                    /    /29\\         /                     /    /29\\\                    /    /29\\
      |                       |atan|--|||                    |atan|--||         |                     |atan|--|||                    |atan|--||         |                       |atan|--|||                    |atan|--||         |                     |atan|--|||                    |atan|--||
      |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|         |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|         |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|         |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|
      |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|         |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|         |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|         |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|
3     |  3                    \   2    /|                    \   2    /   3     |3                    \   2    /|                    \   2    /   3     |  3                    \   2    /|                    \   2    /   3     |3                    \   2    /|                    \   2    /
- + I*|- - + ---------------------------| - --------------------------- + - + I*|- + ---------------------------| + --------------------------- + - + I*|- - - ---------------------------| + --------------------------- + - + I*|- - ---------------------------| - ---------------------------
2     \  2                2             /                2                2     \2                2             /                2                2     \  2                2             /                2                2     \2                2             /                2

\left(- \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2}\right)\right) + \left(\left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} - \frac{3}{2}\right)\right) + \left(\left(- \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)\right) + \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)\right)\right)\right)

      /                       /    /29\\\     /                       /    /29\\\     /                     /    /29\\\     /                     /    /29\\\
      |                       |atan|--|||     |                       |atan|--|||     |                     |atan|--|||     |                     |atan|--|||
      |        ___ 4 _____    |    \12/||     |        ___ 4 _____    |    \12/||     |      ___ 4 _____    |    \12/||     |      ___ 4 _____    |    \12/||
      |      \/ 2 *\/ 985 *sin|--------||     |      \/ 2 *\/ 985 *sin|--------||     |    \/ 2 *\/ 985 *sin|--------||     |    \/ 2 *\/ 985 *sin|--------||
      |  3                    \   2    /|     |  3                    \   2    /|     |3                    \   2    /|     |3                    \   2    /|
6 + I*|- - + ---------------------------| + I*|- - - ---------------------------| + I*|- + ---------------------------| + I*|- - ---------------------------|
      \  2                2             /     \  2                2             /     \2                2             /     \2                2             /

6 + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} - \frac{3}{2}\right) + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2}\right) + i \left(- \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right) + i \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)

producto

/      /                       /    /29\\\                    /    /29\\\ /      /                     /    /29\\\                    /    /29\\\ /      /                       /    /29\\\                    /    /29\\\ /      /                     /    /29\\\                    /    /29\\\
|      |                       |atan|--|||                    |atan|--||| |      |                     |atan|--|||                    |atan|--||| |      |                       |atan|--|||                    |atan|--||| |      |                     |atan|--|||                    |atan|--|||
|      |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|| |      |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|| |      |        ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/|| |      |      ___ 4 _____    |    \12/||     ___ 4 _____    |    \12/||
|      |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|| |      |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|| |      |      \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------|| |      |    \/ 2 *\/ 985 *sin|--------||   \/ 2 *\/ 985 *cos|--------||
|3     |  3                    \   2    /|                    \   2    /| |3     |3                    \   2    /|                    \   2    /| |3     |  3                    \   2    /|                    \   2    /| |3     |3                    \   2    /|                    \   2    /|
|- + I*|- - + ---------------------------| - ---------------------------|*|- + I*|- + ---------------------------| + ---------------------------|*|- + I*|- - - ---------------------------| + ---------------------------|*|- + I*|- - ---------------------------| - ---------------------------|
\2     \  2                2             /                2             / \2     \2                2             /                2             / \2     \  2                2             /                2             / \2     \2                2             /                2             /

\left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2}\right)\right) \left(\frac{3}{2} + \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} - \frac{3}{2}\right)\right) \left(- \frac{\sqrt{2} \sqrt[4]{985} \cos{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{985} \sin{\left(\frac{\operatorname{atan}{\left(\frac{29}{12} \right)}}{2} \right)}}{2} + \frac{3}{2}\right)\right)

136

Respuesta numérica [src]

x1 = -1.79335352084127 - 0.701403509863107*i

x2 = -1.79335352084127 + 0.701403509863107*i

x3 = 4.79335352084127 - 3.70140350986311*i

x4 = 4.79335352084127 + 3.70140350986311*i

x4 = 4.79335352084127 + 3.70140350986311*i

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

(x^2+4)^2+(x^2-6*x-16)^2=0 la ecuación

Solución numérica:

Solución