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(x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720

(x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src] 
/ 2          \ / 2           \ / 2           \      
\x  - 3*x + 2/*\x  - 9*x + 20/*\x  - 9*x + 18/ = 720
((x2−9x)+20)((x2−3x)+2)((x2−9x)+18)=720\left(\left(x^{2} - 9 x\right) + 20\right) \left(\left(x^{2} - 3 x\right) + 2\right) \left(\left(x^{2} - 9 x\right) + 18\right) = 720
Simplificar
Gráfica
05-15-10-510152025-500000010000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 7
x2=7x_{2} = 7 
                        /    /    ____\\                    /    /    ____\\
                        |    |8*\/ 14 ||                    |    |8*\/ 14 ||
                        |atan|--------||                    |atan|--------||
          3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|
         3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|
     7                  \      2       /                    \      2       /
x3 = - - ------------------------------- + ---------------------------------
     2                  2                                  2
x3=−334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2x_{3} = - \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} 
                        /    /    ____\\                    /    /    ____\\
                        |    |8*\/ 14 ||                    |    |8*\/ 14 ||
                        |atan|--------||                    |atan|--------||
          3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|
         3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|
     7                  \      2       /                    \      2       /
x4 = - + ------------------------------- - ---------------------------------
     2                  2                                  2
x4=334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2x_{4} = \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} 
                        /    /    ____\\                    /    /    ____\\
                        |    |8*\/ 14 ||                    |    |8*\/ 14 ||
                        |atan|--------||                    |atan|--------||
          3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|
         3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|
     7                  \      2       /                    \      2       /
x5 = - - ------------------------------- - ---------------------------------
     2                  2                                  2
x5=−334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2x_{5} = - \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} 
                        /    /    ____\\                    /    /    ____\\
                        |    |8*\/ 14 ||                    |    |8*\/ 14 ||
                        |atan|--------||                    |atan|--------||
          3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|
         3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|
     7                  \      2       /                    \      2       /
x6 = - + ------------------------------- + ---------------------------------
     2                  2                                  2
x6=334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2x_{6} = \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} 
x6 = 3^(3/4)*35^(1/4)*sin(atan(8*sqrt(14)/7)/2)/2 + 7/2 + 3^(3/4)*35^(1/4)*i*cos(atan(8*sqrt(14)/7)/2)/2
Suma y producto de raíces [src] 
suma
                       /    /    ____\\                    /    /    ____\\                      /    /    ____\\                    /    /    ____\\                      /    /    ____\\                    /    /    ____\\                      /    /    ____\\                    /    /    ____\\
                       |    |8*\/ 14 ||                    |    |8*\/ 14 ||                      |    |8*\/ 14 ||                    |    |8*\/ 14 ||                      |    |8*\/ 14 ||                    |    |8*\/ 14 ||                      |    |8*\/ 14 ||                    |    |8*\/ 14 ||
                       |atan|--------||                    |atan|--------||                      |atan|--------||                    |atan|--------||                      |atan|--------||                    |atan|--------||                      |atan|--------||                    |atan|--------||
         3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|        3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|        3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|        3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|
        3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|       3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|       3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|       3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|
    7                  \      2       /                    \      2       /   7                  \      2       /                    \      2       /   7                  \      2       /                    \      2       /   7                  \      2       /                    \      2       /
7 + - - ------------------------------- + --------------------------------- + - + ------------------------------- - --------------------------------- + - - ------------------------------- - --------------------------------- + - + ------------------------------- + ---------------------------------
    2                  2                                  2                   2                  2                                  2                   2                  2                                  2                   2                  2                                  2
((−334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2)+((334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2)+(7+(−334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2))))+(334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2)\left(\left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) + \left(\left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) + \left(7 + \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right)\right)\right)\right) + \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) 
=
21
2121 
producto
    /                   /    /    ____\\                    /    /    ____\\\ /                   /    /    ____\\                    /    /    ____\\\ /                   /    /    ____\\                    /    /    ____\\\ /                   /    /    ____\\                    /    /    ____\\\
    |                   |    |8*\/ 14 ||                    |    |8*\/ 14 ||| |                   |    |8*\/ 14 ||                    |    |8*\/ 14 ||| |                   |    |8*\/ 14 ||                    |    |8*\/ 14 ||| |                   |    |8*\/ 14 ||                    |    |8*\/ 14 |||
    |                   |atan|--------||                    |atan|--------||| |                   |atan|--------||                    |atan|--------||| |                   |atan|--------||                    |atan|--------||| |                   |atan|--------||                    |atan|--------|||
    |     3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|| |     3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|| |     3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /|| |     3/4 4 ____    |    \   7    /|      3/4 4 ____    |    \   7    /||
    |    3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|| |    3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|| |    3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------|| |    3   *\/ 35 *sin|--------------|   I*3   *\/ 35 *cos|--------------||
    |7                  \      2       /                    \      2       /| |7                  \      2       /                    \      2       /| |7                  \      2       /                    \      2       /| |7                  \      2       /                    \      2       /|
0*7*|- - ------------------------------- + ---------------------------------|*|- + ------------------------------- - ---------------------------------|*|- - ------------------------------- - ---------------------------------|*|- + ------------------------------- + ---------------------------------|
    \2                  2                                  2                / \2                  2                                  2                / \2                  2                                  2                / \2                  2                                  2                /
0⋅7(−334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2)(334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2)(−334354sin⁡(atan⁡(8147)2)2+72−334354icos⁡(atan⁡(8147)2)2)(334354sin⁡(atan⁡(8147)2)2+72+334354icos⁡(atan⁡(8147)2)2)0 \cdot 7 \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(- \frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} - \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) \left(\frac{3^{\frac{3}{4}} \sqrt[4]{35} \sin{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2} + \frac{7}{2} + \frac{3^{\frac{3}{4}} \sqrt[4]{35} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{8 \sqrt{14}}{7} \right)}}{2} \right)}}{2}\right) 
=
0
00 
0
Respuesta numérica [src] 
x1 = 1.77732575997815 - 2.17200518812337*i
x2 = 1.77732575997815 + 2.17200518812337*i
x3 = 5.22267424002185 + 2.17200518812337*i
x4 = 7.0
x5 = 5.22267424002185 - 2.17200518812337*i
x6 = 0.0
x6 = 0.0
Gráfico
(x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 la ecuación
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