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(x^2-2x+3)sqrt(2x-1)-2(x-2)(2x^2-10x+9)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
/ 2          \   _________             /   2           \    
\x  - 2*x + 3/*\/ 2*x - 1  - 2*(x - 2)*\2*x  - 10*x + 9/ = 0
−2(x−2)((2x2−10x)+9)+2x−1((x2−2x)+3)=0- 2 \left(x - 2\right) \left(\left(2 x^{2} - 10 x\right) + 9\right) + \sqrt{2 x - 1} \left(\left(x^{2} - 2 x\right) + 3\right) = 0
Simplificar
Gráfica
-7.5-5.0-2.50.02.55.07.522.510.012.515.017.520.0-1000010000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 5
x1=5x_{1} = 5 
            /                            /    /      ___\\\                   /    /      ___\\
            |                            |    |147*\/ 7 |||                   |    |147*\/ 7 ||
            |                            |atan|---------|||                   |atan|---------||
            |              ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|
            |      ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|
     65     |  3*\/ 7                    \       2       /|                   \       2       /
x2 = -- + I*|- ------- + ---------------------------------| - ---------------------------------
     32     \     32                     4                /                   4
x2=−2374cos⁡(atan⁡(147717)2)4+6532+i(−3732+2374sin⁡(atan⁡(147717)2)4)x_{2} = - \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{3 \sqrt{7}}{32} + \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4}\right) 
            /                          /    /      ___\\\                   /    /      ___\\
            |                          |    |147*\/ 7 |||                   |    |147*\/ 7 ||
            |                          |atan|---------|||                   |atan|---------||
            |            ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|
            |    ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|
     65     |3*\/ 7                    \       2       /|                   \       2       /
x3 = -- + I*|------- - ---------------------------------| - ---------------------------------
     32     \   32                     4                /                   4
x3=−2374cos⁡(atan⁡(147717)2)4+6532+i(−2374sin⁡(atan⁡(147717)2)4+3732)x_{3} = - \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{3 \sqrt{7}}{32}\right) 
x3 = -sqrt(2)*37^(1/4)*cos(atan(147*sqrt(7)/17)/2)/4 + 65/32 + i*(-sqrt(2)*37^(1/4)*sin(atan(147*sqrt(7)/17)/2)/4 + 3*sqrt(7)/32)
Suma y producto de raíces [src] 
suma
           /                            /    /      ___\\\                   /    /      ___\\          /                          /    /      ___\\\                   /    /      ___\\
           |                            |    |147*\/ 7 |||                   |    |147*\/ 7 ||          |                          |    |147*\/ 7 |||                   |    |147*\/ 7 ||
           |                            |atan|---------|||                   |atan|---------||          |                          |atan|---------|||                   |atan|---------||
           |              ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|          |            ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|
           |      ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|          |    ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|
    65     |  3*\/ 7                    \       2       /|                   \       2       /   65     |3*\/ 7                    \       2       /|                   \       2       /
5 + -- + I*|- ------- + ---------------------------------| - --------------------------------- + -- + I*|------- - ---------------------------------| - ---------------------------------
    32     \     32                     4                /                   4                   32     \   32                     4                /                   4
(−2374cos⁡(atan⁡(147717)2)4+6532+i(−2374sin⁡(atan⁡(147717)2)4+3732))+(5+(−2374cos⁡(atan⁡(147717)2)4+6532+i(−3732+2374sin⁡(atan⁡(147717)2)4)))\left(- \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{3 \sqrt{7}}{32}\right)\right) + \left(5 + \left(- \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{3 \sqrt{7}}{32} + \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4}\right)\right)\right) 
=
        /                            /    /      ___\\\     /                          /    /      ___\\\                   /    /      ___\\
        |                            |    |147*\/ 7 |||     |                          |    |147*\/ 7 |||                   |    |147*\/ 7 ||
        |                            |atan|---------|||     |                          |atan|---------|||                   |atan|---------||
        |              ___ 4 ____    |    \    17   /||     |            ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|
        |      ___   \/ 2 *\/ 37 *sin|---------------||     |    ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|
145     |  3*\/ 7                    \       2       /|     |3*\/ 7                    \       2       /|                   \       2       /
--- + I*|- ------- + ---------------------------------| + I*|------- - ---------------------------------| - ---------------------------------
 16     \     32                     4                /     \   32                     4                /                   2
−2374cos⁡(atan⁡(147717)2)2+14516+i(−2374sin⁡(atan⁡(147717)2)4+3732)+i(−3732+2374sin⁡(atan⁡(147717)2)4)- \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{2} + \frac{145}{16} + i \left(- \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{3 \sqrt{7}}{32}\right) + i \left(- \frac{3 \sqrt{7}}{32} + \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4}\right) 
producto
  /       /                            /    /      ___\\\                   /    /      ___\\\ /       /                          /    /      ___\\\                   /    /      ___\\\
  |       |                            |    |147*\/ 7 |||                   |    |147*\/ 7 ||| |       |                          |    |147*\/ 7 |||                   |    |147*\/ 7 |||
  |       |                            |atan|---------|||                   |atan|---------||| |       |                          |atan|---------|||                   |atan|---------|||
  |       |              ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /|| |       |            ___ 4 ____    |    \    17   /||     ___ 4 ____    |    \    17   /||
  |       |      ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------|| |       |    ___   \/ 2 *\/ 37 *sin|---------------||   \/ 2 *\/ 37 *cos|---------------||
  |65     |  3*\/ 7                    \       2       /|                   \       2       /| |65     |3*\/ 7                    \       2       /|                   \       2       /|
5*|-- + I*|- ------- + ---------------------------------| - ---------------------------------|*|-- + I*|------- - ---------------------------------| - ---------------------------------|
  \32     \     32                     4                /                   4                / \32     \   32                     4                /                   4                /
5(−2374cos⁡(atan⁡(147717)2)4+6532+i(−3732+2374sin⁡(atan⁡(147717)2)4))(−2374cos⁡(atan⁡(147717)2)4+6532+i(−2374sin⁡(atan⁡(147717)2)4+3732))5 \left(- \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{3 \sqrt{7}}{32} + \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4}\right)\right) \left(- \frac{\sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{65}{32} + i \left(- \frac{\sqrt{2} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{4} + \frac{3 \sqrt{7}}{32}\right)\right) 
=
                                     /    /      ___\\                       /    /      ___\\
                                     |    |147*\/ 7 ||                       |    |147*\/ 7 ||
                                     |atan|---------||                       |atan|---------||
                       ___ 4 ____    |    \    17   /|        ____ 4 ____    |    \    17   /|
          ____   325*\/ 2 *\/ 37 *cos|---------------|   15*\/ 14 *\/ 37 *sin|---------------|
335   5*\/ 37                        \       2       /                       \       2       /
--- + -------- - ------------------------------------- - -------------------------------------
 16      8                         64                                      64
−3252374cos⁡(atan⁡(147717)2)64−1514374sin⁡(atan⁡(147717)2)64+5378+33516- \frac{325 \sqrt{2} \sqrt[4]{37} \cos{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{64} - \frac{15 \sqrt{14} \sqrt[4]{37} \sin{\left(\frac{\operatorname{atan}{\left(\frac{147 \sqrt{7}}{17} \right)}}{2} \right)}}{64} + \frac{5 \sqrt{37}}{8} + \frac{335}{16} 
335/16 + 5*sqrt(37)/8 - 325*sqrt(2)*37^(1/4)*cos(atan(147*sqrt(7)/17)/2)/64 - 15*sqrt(14)*37^(1/4)*sin(atan(147*sqrt(7)/17)/2)/64
Respuesta numérica [src] 
x1 = 1.40134983279592 - 0.354929383953914*i
x2 = 1.40134983279598 + 0.354929383953989*i
x3 = 1.40134983279599 - 0.354929383953991*i
x4 = 1.40134983279599 - 0.354929383953991*i
x5 = 1.40134983279601 - 0.35492938395397*i
x6 = 1.40134983279599 - 0.354929383953992*i
x7 = 1.40134983279599 - 0.354929383953992*i
x8 = 5.0
x9 = 1.401349832796 - 0.354929383953951*i
x9 = 1.401349832796 - 0.354929383953951*i
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