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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
dos *((((x- dos)^ dos)/ cuatro)+(veinticinco /(x- dos)^ dos))=(x- dos)/ dos - cinco /(x- dos)
2 multiplicar por ((((x menos 2) al cuadrado ) dividir por 4) más (25 dividir por (x menos 2) al cuadrado )) es igual a (x menos 2) dividir por 2 menos 5 dividir por (x menos 2)
dos multiplicar por ((((x menos dos) en el grado dos) dividir por cuatro) más (veinticinco dividir por (x menos dos) en el grado dos)) es igual a (x menos dos) dividir por dos menos cinco dividir por (x menos dos)
2*((((x-2)2)/4)+(25/(x-2)2))=(x-2)/2-5/(x-2)
2*x-22/4+25/x-22=x-2/2-5/x-2
2*((((x-2)²)/4)+(25/(x-2)²))=(x-2)/2-5/(x-2)
2*((((x-2) en el grado 2)/4)+(25/(x-2) en el grado 2))=(x-2)/2-5/(x-2)
2((((x-2)^2)/4)+(25/(x-2)^2))=(x-2)/2-5/(x-2)
2((((x-2)2)/4)+(25/(x-2)2))=(x-2)/2-5/(x-2)
2x-22/4+25/x-22=x-2/2-5/x-2
2x-2^2/4+25/x-2^2=x-2/2-5/x-2
2*((((x-2)^2) dividir por 4)+(25 dividir por (x-2)^2))=(x-2) dividir por 2-5 dividir por (x-2)
Expresiones semejantes
2*((((x+2)^2)/4)+(25/(x-2)^2))=(x-2)/2-5/(x-2)
2*((((x-2)^2)/4)+(25/(x-2)^2))=(x-2)/2+5/(x-2)
2*((((x-2)^2)/4)-(25/(x-2)^2))=(x-2)/2-5/(x-2)
2*((((x-2)^2)/4)+(25/(x-2)^2))=(x+2)/2-5/(x-2)
2*((((x-2)^2)/4)+(25/(x+2)^2))=(x-2)/2-5/(x-2)
2*((((x-2)^2)/4)+(25/(x-2)^2))=(x-2)/2-5/(x+2)

2*((((x-2)^2)/4)+(25/(x-2)^2))=(x-2)/2-5/(x-2) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

  /       2           \                
  |(x - 2)       25   |   x - 2     5  
2*|-------- + --------| = ----- - -----
  |   4              2|     2     x - 2
  \           (x - 2) /

2 \left(\frac{\left(x - 2\right)^{2}}{4} + \frac{25}{\left(x - 2\right)^{2}}\right) = \frac{x - 2}{2} - \frac{5}{x - 2}

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

           /                          /    /  ____\\\                  /    /  ____\\
           |                          |    |\/ 79 |||                  |    |\/ 79 ||
           |                          |atan|------|||                  |atan|------||
           |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|
           |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|
     9     |  \/ 79                   \     2      /|                  \     2      /
x1 = - + I*|- ------ + -----------------------------| - -----------------------------
     4     \    4                    2              /                 2

x_{1} = - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{\sqrt{79}}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)

           /                          /    /  ____\\\                  /    /  ____\\
           |                          |    |\/ 79 |||                  |    |\/ 79 ||
           |                          |atan|------|||                  |atan|------||
           |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|
           |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|
     9     |  \/ 79                   \     2      /|                  \     2      /
x2 = - + I*|- ------ - -----------------------------| + -----------------------------
     4     \    4                    2              /                 2

x_{2} = \frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{79}}{4} - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)

           /                        /    /  ____\\\                  /    /  ____\\
           |                        |    |\/ 79 |||                  |    |\/ 79 ||
           |                        |atan|------|||                  |atan|------||
           |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|
           |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|
     9     |\/ 79                   \     2      /|                  \     2      /
x3 = - + I*|------ - -----------------------------| - -----------------------------
     4     \  4                    2              /                 2

x_{3} = - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)

           /                        /    /  ____\\\                  /    /  ____\\
           |                        |    |\/ 79 |||                  |    |\/ 79 ||
           |                        |atan|------|||                  |atan|------||
           |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|
           |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|
     9     |\/ 79                   \     2      /|                  \     2      /
x4 = - + I*|------ + -----------------------------| + -----------------------------
     4     \  4                    2              /                 2

x_{4} = \frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(\frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)

x4 = 9/4 + 2^(3/4)*55^(1/4)*cos(atan(sqrt(79)/41)/2)/2 + i*(2^(3/4)*55^(1/4)*sin(atan(sqrt(79)/41)/2)/2 + sqrt(79)/4)

Suma y producto de raíces [src]

suma

      /                          /    /  ____\\\                  /    /  ____\\         /                          /    /  ____\\\                  /    /  ____\\         /                        /    /  ____\\\                  /    /  ____\\         /                        /    /  ____\\\                  /    /  ____\\
      |                          |    |\/ 79 |||                  |    |\/ 79 ||         |                          |    |\/ 79 |||                  |    |\/ 79 ||         |                        |    |\/ 79 |||                  |    |\/ 79 ||         |                        |    |\/ 79 |||                  |    |\/ 79 ||
      |                          |atan|------|||                  |atan|------||         |                          |atan|------|||                  |atan|------||         |                        |atan|------|||                  |atan|------||         |                        |atan|------|||                  |atan|------||
      |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|         |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|         |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|         |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|
      |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|         |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|         |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|         |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|
9     |  \/ 79                   \     2      /|                  \     2      /   9     |  \/ 79                   \     2      /|                  \     2      /   9     |\/ 79                   \     2      /|                  \     2      /   9     |\/ 79                   \     2      /|                  \     2      /
- + I*|- ------ + -----------------------------| - ----------------------------- + - + I*|- ------ - -----------------------------| + ----------------------------- + - + I*|------ - -----------------------------| - ----------------------------- + - + I*|------ + -----------------------------| + -----------------------------
4     \    4                    2              /                 2                 4     \    4                    2              /                 2                 4     \  4                    2              /                 2                 4     \  4                    2              /                 2

\left(\left(\left(\frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{79}}{4} - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)\right) + \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{\sqrt{79}}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)\right)\right) + \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)\right)\right) + \left(\frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(\frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)\right)

      /                          /    /  ____\\\     /                          /    /  ____\\\     /                        /    /  ____\\\     /                        /    /  ____\\\
      |                          |    |\/ 79 |||     |                          |    |\/ 79 |||     |                        |    |\/ 79 |||     |                        |    |\/ 79 |||
      |                          |atan|------|||     |                          |atan|------|||     |                        |atan|------|||     |                        |atan|------|||
      |            3/4 4 ____    |    \  41  /||     |            3/4 4 ____    |    \  41  /||     |          3/4 4 ____    |    \  41  /||     |          3/4 4 ____    |    \  41  /||
      |    ____   2   *\/ 55 *sin|------------||     |    ____   2   *\/ 55 *sin|------------||     |  ____   2   *\/ 55 *sin|------------||     |  ____   2   *\/ 55 *sin|------------||
      |  \/ 79                   \     2      /|     |  \/ 79                   \     2      /|     |\/ 79                   \     2      /|     |\/ 79                   \     2      /|
9 + I*|- ------ + -----------------------------| + I*|- ------ - -----------------------------| + I*|------ + -----------------------------| + I*|------ - -----------------------------|
      \    4                    2              /     \    4                    2              /     \  4                    2              /     \  4                    2              /

9 + i \left(- \frac{\sqrt{79}}{4} - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right) + i \left(- \frac{\sqrt{79}}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right) + i \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right) + i \left(\frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)

producto

/      /                          /    /  ____\\\                  /    /  ____\\\ /      /                          /    /  ____\\\                  /    /  ____\\\ /      /                        /    /  ____\\\                  /    /  ____\\\ /      /                        /    /  ____\\\                  /    /  ____\\\
|      |                          |    |\/ 79 |||                  |    |\/ 79 ||| |      |                          |    |\/ 79 |||                  |    |\/ 79 ||| |      |                        |    |\/ 79 |||                  |    |\/ 79 ||| |      |                        |    |\/ 79 |||                  |    |\/ 79 |||
|      |                          |atan|------|||                  |atan|------||| |      |                          |atan|------|||                  |atan|------||| |      |                        |atan|------|||                  |atan|------||| |      |                        |atan|------|||                  |atan|------|||
|      |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|| |      |            3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|| |      |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /|| |      |          3/4 4 ____    |    \  41  /||    3/4 4 ____    |    \  41  /||
|      |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|| |      |    ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|| |      |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------|| |      |  ____   2   *\/ 55 *sin|------------||   2   *\/ 55 *cos|------------||
|9     |  \/ 79                   \     2      /|                  \     2      /| |9     |  \/ 79                   \     2      /|                  \     2      /| |9     |\/ 79                   \     2      /|                  \     2      /| |9     |\/ 79                   \     2      /|                  \     2      /|
|- + I*|- ------ + -----------------------------| - -----------------------------|*|- + I*|- ------ - -----------------------------| + -----------------------------|*|- + I*|------ - -----------------------------| - -----------------------------|*|- + I*|------ + -----------------------------| + -----------------------------|
\4     \    4                    2              /                 2              / \4     \    4                    2              /                 2              / \4     \  4                    2              /                 2              / \4     \  4                    2              /                 2              /

\left(\frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{79}}{4} - \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{\sqrt{79}}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{9}{4} + i \left(- \frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)\right) \left(\frac{9}{4} + \frac{2^{\frac{3}{4}} \sqrt[4]{55} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + i \left(\frac{2^{\frac{3}{4}} \sqrt[4]{55} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{79}}{41} \right)}}{2} \right)}}{2} + \frac{\sqrt{79}}{4}\right)\right)

104

Respuesta numérica [src]

x1 = -0.0269545714452405 - 1.97807704773801*i

x2 = 4.52695457144524 - 2.46602016091978*i

x3 = -0.0269545714452405 + 1.97807704773801*i

x4 = 4.52695457144524 + 2.46602016091978*i

x4 = 4.52695457144524 + 2.46602016091978*i

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

2*((((x-2)^2)/4)+(25/(x-2)^2))=(x-2)/2-5/(x-2) la ecuación

Solución numérica:

Solución