Question

Qual a Solução da BIQUADRADA 8x4 - 10x² + 3 = 0

Answer 1

Resposta:

Para;

$x^{4} =y^{2} \\x^{2} =y\\8y^{2} -10y+3=0$

Δ = (10)² - 4 × 8 × 3

Δ = 100 - 96

Δ = 4

$y'=\frac{-b+\sqrt{delta}}{2*a} \\y'=\frac{-(10)+\sqrt{4}}{2*8}\\x'=\frac{10+2}{16}\\x'=\frac{12:4}{16:4}\\y'=\frac{3}{4}\\\\y"=\frac{-b-\sqrt{delta}}{2*a}\\y"=\frac{10-\sqrt{4}}{2*8}\\y"=\frac{10-2}{16}\\y"=\frac{8:8}{16:8}\\\\y"=\frac{1}{2}$

Conjunto verdade;

$[-\frac{1}{2},-\frac{3}{4},\frac{3}{4},\frac{1}{2}]$

$y'=\frac{3}{4}\\x^{2}=y\\x^{2}=\frac{3}{4}\\x=\frac{\sqrt{3}}{\sqrt{4}}=[\frac{\sqrt{3}}{2}]ou[-\frac{\sqrt{3}}{2}]\\\\y"=\frac{1}{2}\\x^{2}=y\\x^{2}=\frac{1}{2}\\x=\frac{\sqrt{1}}{\sqrt{2}}=\frac{1*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{4}}\\x=[\frac{\sqrt{2}}{2}]ou[-\frac{\sqrt{2}}{2}]$

Explicação passo-a-passo: