Question

DESAFIO EQUAÇÃO
Resolva a equação (3x²-4)^4/3=16

Answer 1

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Ola Shai

(3x² - 4)^(4/3) = 16

(3x² - 4)^4 = 4096

(3x² - 4) = 8

3x² = 12

x² = 4

x1 = -2
x2 = 2

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Answer 2

Oie, Td Bom?!

$(3x {}^{2} - 4) {}^{ \frac{4}{3} } = 16 \\ \\ \sqrt[3]{(3x {}^{2} - 4) {}^{4} } = 16 \\ \\ \sqrt[3]{(3x {}^{2} - 4) {}^{4} } {}^{3} = 16 {}^{3} \\ \\ (3x {}^{2} - 4) {}^{4} = 4096 \\ \\ 3x {}^{2} - 4 = ± \sqrt[4]{4096} \\ \\ 3x {}^{2} - 4 = ±8$

$3x {}^{2} - 4 = - 8 \\ 3x {}^{2} = - 8 + 4 \\ 3x {}^{2} = - 4 \\ \\ x∉\mathbb{R} \\ \\ 3x {}^{2} - 4 = 8 \\ 3x {}^{2} = 8 + 4 \\ 3x {}^{2} = 12 \\ x {}^{2} = 4 \\ x = ±2 \\ \\ x = - 2 \\ x = 2$

S = $\left \{x_{1} = - 2 \: , \: x_{2} = 2 \right \}$

Att. Makaveli1996