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log(7x^4-(x^4-9)^(1/2)+x^2+8)=log(x^8-(x^4-9)^(1/2)+x^2-10) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /          ________         \      /        ________          \
   |   4     /  4         2    |      | 8     /  4         2     |
log\7*x  - \/  x  - 9  + x  + 8/ = log\x  - \/  x  - 9  + x  - 10/
log⁡((x2+(7x4−x4−9))+8)=log⁡((x2+(x8−x4−9))−10)\log{\left(\left(x^{2} + \left(7 x^{4} - \sqrt{x^{4} - 9}\right)\right) + 8 \right)} = \log{\left(\left(x^{2} + \left(x^{8} - \sqrt{x^{4} - 9}\right)\right) - 10 \right)}
Simplificar
Gráfica
02468-10-8-6-4-210040
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
        ___
x1 = -\/ 3
x1=−3x_{1} = - \sqrt{3} 
       ___
x2 = \/ 3
x2=3x_{2} = \sqrt{3} 
        3/4      3/4
       2      I*2   
x3 = - ---- + ------
        2       2
x3=−2342+234i2x_{3} = - \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2} 
      3/4      3/4
     2      I*2   
x4 = ---- - ------
      2       2
x4=2342−234i2x_{4} = \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2} 
        3/4      3/4
       2      I*2   
x5 = - ---- - ------
        2       2
x5=−2342−234i2x_{5} = - \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2} 
      3/4      3/4
     2      I*2   
x6 = ---- + ------
      2       2
x6=2342+234i2x_{6} = \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2} 
          ___
x7 = -I*\/ 3
x7=−3ix_{7} = - \sqrt{3} i 
         ___
x8 = I*\/ 3
x8=3ix_{8} = \sqrt{3} i 
x8 = sqrt(3)*i
Suma y producto de raíces [src] 
suma
                     3/4      3/4    3/4      3/4      3/4      3/4    3/4      3/4                    
    ___     ___     2      I*2      2      I*2        2      I*2      2      I*2          ___       ___
- \/ 3  + \/ 3  + - ---- + ------ + ---- - ------ + - ---- - ------ + ---- + ------ - I*\/ 3  + I*\/ 3 
                     2       2       2       2         2       2       2       2
(−3i+(((−2342−234i2)+((2342−234i2)+((−3+3)+(−2342+234i2))))+(2342+234i2)))+3i\left(- \sqrt{3} i + \left(\left(\left(- \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right) + \left(\left(\frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right) + \left(\left(- \sqrt{3} + \sqrt{3}\right) + \left(- \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right)\right)\right) + \left(\frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right)\right) + \sqrt{3} i 
=
0
00 
producto
             /   3/4      3/4\ / 3/4      3/4\ /   3/4      3/4\ / 3/4      3/4\                   
   ___   ___ |  2      I*2   | |2      I*2   | |  2      I*2   | |2      I*2   | /     ___\     ___
-\/ 3 *\/ 3 *|- ---- + ------|*|---- - ------|*|- ---- - ------|*|---- + ------|*\-I*\/ 3 /*I*\/ 3 
             \   2       2   / \ 2       2   / \   2       2   / \ 2       2   /
3i−3i−33(−2342+234i2)(2342−234i2)(−2342−234i2)(2342+234i2)\sqrt{3} i - \sqrt{3} i - \sqrt{3} \sqrt{3} \left(- \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right) \left(\frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right) \left(- \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right) \left(\frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right) 
=
-18
−18-18 
-18
Respuesta numérica [src] 
x1 = -1.73205080756888
x2 = 1.73205080756888
x3 = -0.840896415253715 + 0.840896415253715*i
x4 = 0.840896415253715 - 0.840896415253715*i
x5 = -0.840896415253715 - 0.840896415253715*i
x6 = 0.840896415253715 + 0.840896415253715*i
x7 = -1.73205080756888*i
x8 = 1.73205080756888*i
x8 = 1.73205080756888*i
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