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La ecuación:
Ecuación -x/11+x=50/11
Ecuación 12/x=3
Ecuación 6-5(4x-1)=3
Ecuación 13/(x-5)=5/(x-13)
Expresar {x} en función de y en la ecuación:
-1*x+4*y=-10
-11*x-19*y=14
8*x+6*y=20
-11*x-1*y=15
Expresiones idénticas
*x^ dos + quince *x+ dos *sqrt(x^ dos + cinco *x+ uno)= dos
multiplicar por x al cuadrado más 15 multiplicar por x más 2 multiplicar por raíz cuadrada de (x al cuadrado más 5 multiplicar por x más 1) es igual a 2
multiplicar por x en el grado dos más quince multiplicar por x más dos multiplicar por raíz cuadrada de (x en el grado dos más cinco multiplicar por x más uno) es igual a dos
*x^2+15*x+2*√(x^2+5*x+1)=2
*x2+15*x+2*sqrt(x2+5*x+1)=2
*x2+15*x+2*sqrtx2+5*x+1=2
*x²+15*x+2*sqrt(x²+5*x+1)=2
*x en el grado 2+15*x+2*sqrt(x en el grado 2+5*x+1)=2
x^2+15x+2sqrt(x^2+5x+1)=2
x2+15x+2sqrt(x2+5x+1)=2
x2+15x+2sqrtx2+5x+1=2
x^2+15x+2sqrtx^2+5x+1=2
Expresiones semejantes
*x^2+15*x-2*sqrt(x^2+5*x+1)=2
*x^2+15*x+2*sqrt(x^2-5*x+1)=2
*x^2+15*x+2*sqrt(x^2+5*x-1)=2
*x^2-15*x+2*sqrt(x^2+5*x+1)=2
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x-a)+abs(x+a)=4
sqrt^4(17x^2-16)=x
sqrt4(4x+5-x^2)-sqrt(4x-x^2-3)=1
sqrt(log(cos(x)))=0
sqrt(x^3+x^2+1)=sqrt(2*x^2-2*x+1)

x^2+15x+2sqrt(x^2+5x+1)=2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                 ______________    
 2              /  2               
x  + 15*x + 2*\/  x  + 5*x + 1  = 2

\left(x^{2} + 15 x\right) + 2 \sqrt{\left(x^{2} + 5 x\right) + 1} = 2

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

           /                     1                     \     /     /                     1                     \                                                                   \                                                                   
      83*re|-------------------------------------------|     |83*im|-------------------------------------------|             /    /    ________\\              /    /    ________\\|             /    /    ________\\              /    /    ________\\
           |     ______________________                |     |     |     ______________________                |             |    |2*\/ 112434 ||              |    |2*\/ 112434 |||             |    |2*\/ 112434 ||              |    |2*\/ 112434 ||
           |    /             ________  /          ___\|     |     |    /             ________  /          ___\|             |atan|------------||              |atan|------------|||             |atan|------------||              |atan|------------||
           |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     |     |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     ____    |    \    1125    /|     _____    |    \    1125    /||     ____    |    \    1125    /|     _____    |    \    1125    /|
           |3 /   125 + -------------- *|- - - -------||     |     |3 /   125 + -------------- *|- - - -------||   \/ 83 *cos|------------------|   \/ 249 *sin|------------------||   \/ 83 *sin|------------------|   \/ 249 *cos|------------------|
           \\/                9         \  2      2   //     |     \\/                9         \  2      2   //             \        3         /              \        3         /|             \        3         /              \        3         /
-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
                              3                              \                        3                                          2                                 6               /                 2                                 6

-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)

           /                     1                     \     /     /                     1                     \                                                                   \                                                                   
      83*re|-------------------------------------------|     |83*im|-------------------------------------------|             /    /    ________\\              /    /    ________\\|             /    /    ________\\              /    /    ________\\
           |     ______________________                |     |     |     ______________________                |             |    |2*\/ 112434 ||              |    |2*\/ 112434 |||             |    |2*\/ 112434 ||              |    |2*\/ 112434 ||
           |    /             ________  /          ___\|     |     |    /             ________  /          ___\|             |atan|------------||              |atan|------------|||             |atan|------------||              |atan|------------||
           |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     |     |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     ____    |    \    1125    /|     _____    |    \    1125    /||     ____    |    \    1125    /|     _____    |    \    1125    /|
           |3 /   125 + -------------- *|- - - -------||     |     |3 /   125 + -------------- *|- - - -------||   \/ 83 *cos|------------------|   \/ 249 *sin|------------------||   \/ 83 *sin|------------------|   \/ 249 *cos|------------------|
           \\/                9         \  2      2   //     |     \\/                9         \  2      2   //             \        3         /              \        3         /|             \        3         /              \        3         /
-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
                              3                              \                        3                                          2                                 6               /                 2                                 6

-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)

producto

  /           /                     1                     \     /     /                     1                     \                                                                   \                                                                   \
  |      83*re|-------------------------------------------|     |83*im|-------------------------------------------|             /    /    ________\\              /    /    ________\\|             /    /    ________\\              /    /    ________\\|
  |           |     ______________________                |     |     |     ______________________                |             |    |2*\/ 112434 ||              |    |2*\/ 112434 |||             |    |2*\/ 112434 ||              |    |2*\/ 112434 |||
  |           |    /             ________  /          ___\|     |     |    /             ________  /          ___\|             |atan|------------||              |atan|------------|||             |atan|------------||              |atan|------------|||
  |           |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     |     |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     ____    |    \    1125    /|     _____    |    \    1125    /||     ____    |    \    1125    /|     _____    |    \    1125    /||
  |           |3 /   125 + -------------- *|- - - -------||     |     |3 /   125 + -------------- *|- - - -------||   \/ 83 *cos|------------------|   \/ 249 *sin|------------------||   \/ 83 *sin|------------------|   \/ 249 *cos|------------------||
  |           \\/                9         \  2      2   //     |     \\/                9         \  2      2   //             \        3         /              \        3         /|             \        3         /              \        3         /|
0*|-10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------|
  \                              3                              \                        3                                          2                                 6               /                 2                                 6               /

0 \left(-10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)\right)

0

Respuesta rápida [src]

x1 = 0

x_{1} = 0

                /                     1                     \     /     /                     1                     \                                                                   \                                                                   
           83*re|-------------------------------------------|     |83*im|-------------------------------------------|             /    /    ________\\              /    /    ________\\|             /    /    ________\\              /    /    ________\\
                |     ______________________                |     |     |     ______________________                |             |    |2*\/ 112434 ||              |    |2*\/ 112434 |||             |    |2*\/ 112434 ||              |    |2*\/ 112434 ||
                |    /             ________  /          ___\|     |     |    /             ________  /          ___\|             |atan|------------||              |atan|------------|||             |atan|------------||              |atan|------------||
                |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     |     |   /        2*I*\/ 112434   |  1   I*\/ 3 ||     ____    |    \    1125    /|     _____    |    \    1125    /||     ____    |    \    1125    /|     _____    |    \    1125    /|
                |3 /   125 + -------------- *|- - - -------||     |     |3 /   125 + -------------- *|- - - -------||   \/ 83 *cos|------------------|   \/ 249 *sin|------------------||   \/ 83 *sin|------------------|   \/ 249 *cos|------------------|
                \\/                9         \  2      2   //     |     \\/                9         \  2      2   //             \        3         /              \        3         /|             \        3         /              \        3         /
x2 = -10 + -------------------------------------------------- + I*|-------------------------------------------------- - ------------------------------ - -------------------------------| + ------------------------------ - -------------------------------
                                   3                              \                        3                                          2                                 6               /                 2                                 6

x_{2} = -10 - \frac{\sqrt{249} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3} + \frac{\sqrt{83} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} + i \left(- \frac{\sqrt{83} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{2} - \frac{\sqrt{249} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{112434}}{1125} \right)}}{3} \right)}}{6} + \frac{83 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{125 + \frac{2 \sqrt{112434} i}{9}}}\right)}}{3}\right)

x2 = -10 - sqrt(249)*cos(atan(2*sqrt(112434)/1125)/3)/6 + 83*re(1/((-1/2 - sqrt(3)*i/2)*(125 + 2*sqrt(112434)*i/9)^(1/3)))/3 + sqrt(83)*sin(atan(2*sqrt(112434)/1125)/3)/2 + i*(-sqrt(83)*cos(atan(2*sqrt(112434)/1125)/3)/2 - sqrt(249)*sin(atan(2*sqrt(112434)/1125)/3)/6 + 83*im(1/((-1/2 - sqrt(3)*i/2)*(125 + 2*sqrt(112434)*i/9)^(1/3)))/3)

Respuesta numérica [src]

x1 = -13.5519674997921

x2 = 0.0

x2 = 0.0

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

*x^2+15*x+2*sqrt(x^2+5*x+1)=2 la ecuación

Solución numérica:

Solución

x^2+15x+2sqrt(x^2+5x+1)=2 la ecuación