Question

Equação biquadrada
X^4-18x^2+81

Answer 1

x^4-18x^2 + 81= 0

(x^2)^2 -18x^2 +81=0 

x^2= k 

k^2 -18k +81=0

Δ= 324 - 324
Δ=0

k= 18 +ou - √0/2
k = 18 +0/2
k'=k"= 18/2= 9
x^2= 9
x= +ou - √9
x'= √9 = 3  e  x"= - √9 = -3

Answer 2

$x^4 -18x^2+81=0 \\ \\ (x^2)^2 - 18(x^2) +81=0 \\ \\ x^2= y \\ \\ y^2 -18y +81=0 \\ \\ y= \dfrac{-(-18 )\pm \sqrt{(-18)^2-4\cdot1\cdot 81} }{2\cdot 1} \\ \\ \\ y' = y'' =9 \\ \\ x^2=y \rightarrow x^2=9 \rightarrow x=\pm 3 \\ \\ \boxed{S=\left \{-3\, ,\,3 \right \}}$