Question

substituiremos x² por y e x⁴ por y²
-4x⁴ +8x² -4 = 0
(-4y² +8y-4=0) me ajude por favor

Answer 1

Equação Biquadrada:

$-4x^4+8x^2-4=0\to~~x^2=y\\\\ -4y^2+8y-4=0\\\\ a=-4;\ b=8;\ c=-4\\\\\\ \Delta=b^2-4ac\to \Delta=8^2-4.(-4).(-4)\to \Delta=64-64\to \boxed{\Delta=0}\\\\ y'=y''\\\\\\ y= \dfrac{-b\pm \sqrt{\Delta} }{2a} \to y= \dfrac{-8\pm \sqrt{0} }{2.(-4)} \to y= \dfrac{-8\pm 0}{-8} \to \\\\\\ y'=y''= \dfrac{-8}{-8} \to \boxed{ y'=y''=1}$



$x^2=y\to ~~x^2=1\to ~~x=\pm \sqrt{1} \to ~~x=\pm~1\\\\\\\\\\ \boxed{\boxed{S=\{-1~;~1\}}}$