Question

Resolva a equação biquadrada dada por x⁴-26x²+25=0

Answer 1

x^2 = y
x^4 = y^2

y^2 -26y + 25 = 0

Soma = 26 —— y1 = 25
Produto = 25 — y2 = 1

x^2 = y
x^2 = 25
x = +5 ou -5

x^2 = 1
x = +1 ou -1

S = { -5, -1, 1, 5}

Answer 2

$\mathsf{x^4-26x^2+25=0}$

$\mathsf{a=1\quad b=-26\quad c=25}$

$\mathsf{ \Delta=b^2-4\cdot a\cdot c}$

$\mathsf{ \Delta=(-26)^2-4\cdot1\cdot25}$

$\mathsf{\Delta=6 76- 100}$

$\mathsf{ \Delta= 576}$

$\mathsf{x=\pm\sqrt{\dfrac{-b\pm\sqrt\Delta}{2\cdot a}} }$

$\mathsf{x=\pm\sqrt{\dfrac{-(-26)\pm\sqrt{576}}{2\cdot1}} }$

$\mathsf{ x=\pm\sqrt{\dfrac{26\pm24}{2}}\begin{cases}\sf x'=\sqrt{\dfrac{26+24}{2}}=\sqrt{25}=5\\\\\sf x''=-\sqrt{\dfrac{26+24}{2}}=-\sqrt{25}=-5\\\\\sf x'''=\sqrt{\dfrac{26-24}{2}}= \sqrt1=1\\\\\sf x''''=-\sqrt{\dfrac{26-24}{2}}=-\sqrt1=-1\end{cases}}$

$\boxed{\boxed{\mathsf{S=\{-5;\,-1;\,1;\,5\} }}}$