Question

Resolva a equação biquadrada: (x²+10)(x²-10)+36=0

Answer 1

$(x^2+10)(x^2-10)+36=0 \implies (x^2)^2 - 10^2 +36 = 0 \implies x^4-100+36 = 0 \implies x^4-64=0 \implies x^4 - 8^2 = 0 \implies (x^2-8)(x^2+8)=0 \implies$

$x^2-8=0$ ou $x^2+8=0$

Raízes reais:

$x^2-8=0 \implies x^2 = 8 \implies x=\sqrt{8} \implies x=\sqrt{2^3} \implies x = \pm2\sqrt{2}$

Raízes complexas:

$x^2+8=0 \implies x^2 = -8 \implies x=\sqrt{-8} \implies x=\sqrt{(-2)^3} \implies x=\sqrt{(-2)^2.(-2)} \implies x = \pm2\sqrt{-2}$

Answer 2

Resposta:

9

Explicação passo-a-passo:

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