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x^2+10=x*(sqrt(3x+10)-3) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 2          /  __________    \
x  + 10 = x*\\/ 3*x + 10  - 3/
x2+10=x(3x+10−3)x^{2} + 10 = x \left(\sqrt{3 x + 10} - 3\right)
Simplificar
Gráfica
02468-8-6-4-2-1010200-100
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
             /                      /    /     ___\\\               /    /     ___\\
             |                      |    |31*\/ 3 |||               |    |31*\/ 3 ||
             |                      |atan|--------|||               |atan|--------||
             |          4 ______    |    \   49   /||   4 ______    |    \   49   /|
             |    ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------|
       3     |3*\/ 3                \      2       /|               \      2       /
x1 = - - + I*|------- + ----------------------------| + ----------------------------
       4     \   4                   2              /                2
x1=−34+13214sin⁡(atan⁡(31349)2)2+i(334+13214cos⁡(atan⁡(31349)2)2)x_{1} = - \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2}\right) 
             /                        /    /     ___\\\               /    /     ___\\
             |                        |    |31*\/ 3 |||               |    |31*\/ 3 ||
             |                        |atan|--------|||               |atan|--------||
             |            4 ______    |    \   49   /||   4 ______    |    \   49   /|
             |      ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------|
       3     |  3*\/ 3                \      2       /|               \      2       /
x2 = - - + I*|- ------- - ----------------------------| + ----------------------------
       4     \     4                   2              /                2
x2=−34+13214sin⁡(atan⁡(31349)2)2+i(−13214cos⁡(atan⁡(31349)2)2−334)x_{2} = - \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right) 
x2 = -3/4 + 1321^(1/4)*sin(atan(31*sqrt(3)/49)/2)/2 + i*(-1321^(1/4)*cos(atan(31*sqrt(3)/49)/2)/2 - 3*sqrt(3)/4)
Suma y producto de raíces [src] 
suma
        /                      /    /     ___\\\               /    /     ___\\           /                        /    /     ___\\\               /    /     ___\\
        |                      |    |31*\/ 3 |||               |    |31*\/ 3 ||           |                        |    |31*\/ 3 |||               |    |31*\/ 3 ||
        |                      |atan|--------|||               |atan|--------||           |                        |atan|--------|||               |atan|--------||
        |          4 ______    |    \   49   /||   4 ______    |    \   49   /|           |            4 ______    |    \   49   /||   4 ______    |    \   49   /|
        |    ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------|           |      ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------|
  3     |3*\/ 3                \      2       /|               \      2       /     3     |  3*\/ 3                \      2       /|               \      2       /
- - + I*|------- + ----------------------------| + ---------------------------- + - - + I*|- ------- - ----------------------------| + ----------------------------
  4     \   4                   2              /                2                   4     \     4                   2              /                2
(−34+13214sin⁡(atan⁡(31349)2)2+i(−13214cos⁡(atan⁡(31349)2)2−334))+(−34+13214sin⁡(atan⁡(31349)2)2+i(334+13214cos⁡(atan⁡(31349)2)2))\left(- \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right)\right) + \left(- \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2}\right)\right) 
=
        /                        /    /     ___\\\     /                      /    /     ___\\\                               
        |                        |    |31*\/ 3 |||     |                      |    |31*\/ 3 |||                               
        |                        |atan|--------|||     |                      |atan|--------|||               /    /     ___\\
        |            4 ______    |    \   49   /||     |          4 ______    |    \   49   /||               |    |31*\/ 3 ||
        |      ___   \/ 1321 *cos|--------------||     |    ___   \/ 1321 *cos|--------------||               |atan|--------||
  3     |  3*\/ 3                \      2       /|     |3*\/ 3                \      2       /|   4 ______    |    \   49   /|
- - + I*|- ------- - ----------------------------| + I*|------- + ----------------------------| + \/ 1321 *sin|--------------|
  2     \     4                   2              /     \   4                   2              /               \      2       /
−32+13214sin⁡(atan⁡(31349)2)+i(−13214cos⁡(atan⁡(31349)2)2−334)+i(334+13214cos⁡(atan⁡(31349)2)2)- \frac{3}{2} + \sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)} + i \left(- \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right) + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2}\right) 
producto
/        /                      /    /     ___\\\               /    /     ___\\\ /        /                        /    /     ___\\\               /    /     ___\\\
|        |                      |    |31*\/ 3 |||               |    |31*\/ 3 ||| |        |                        |    |31*\/ 3 |||               |    |31*\/ 3 |||
|        |                      |atan|--------|||               |atan|--------||| |        |                        |atan|--------|||               |atan|--------|||
|        |          4 ______    |    \   49   /||   4 ______    |    \   49   /|| |        |            4 ______    |    \   49   /||   4 ______    |    \   49   /||
|        |    ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------|| |        |      ___   \/ 1321 *cos|--------------||   \/ 1321 *sin|--------------||
|  3     |3*\/ 3                \      2       /|               \      2       /| |  3     |  3*\/ 3                \      2       /|               \      2       /|
|- - + I*|------- + ----------------------------| + ----------------------------|*|- - + I*|- ------- - ----------------------------| + ----------------------------|
\  4     \   4                   2              /                2              / \  4     \     4                   2              /                2              /
(−34+13214sin⁡(atan⁡(31349)2)2+i(334+13214cos⁡(atan⁡(31349)2)2))(−34+13214sin⁡(atan⁡(31349)2)2+i(−13214cos⁡(atan⁡(31349)2)2−334))\left(- \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(\frac{3 \sqrt{3}}{4} + \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{3}{4} + \frac{\sqrt[4]{1321} \sin{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{1321} \cos{\left(\frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} \right)}}{2} - \frac{3 \sqrt{3}}{4}\right)\right) 
=
                             /      /     ___\     \
                             |      |31*\/ 3 |     |
                             |  atan|--------|     |
                 4 ______    |      \   49   /   pi|
      ______   3*\/ 1321 *sin|- -------------- + --|
9   \/ 1321                  \        2          3 /
- + -------- + -------------------------------------
4      4                         2
94+313214sin⁡(−atan⁡(31349)2+π3)2+13214\frac{9}{4} + \frac{3 \sqrt[4]{1321} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{31 \sqrt{3}}{49} \right)}}{2} + \frac{\pi}{3} \right)}}{2} + \frac{\sqrt{1321}}{4} 
9/4 + sqrt(1321)/4 + 3*1321^(1/4)*sin(-atan(31*sqrt(3)/49)/2 + pi/3)/2
Respuesta numérica [src] 
x1 = 0.466838305341577 - 4.05688064312265*i
x2 = 0.466838305341577 + 4.05688064312265*i
x2 = 0.466838305341577 + 4.05688064312265*i
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