Question

Oí Por favor

Resolva em lR :
$x^{4} - 7x^{2} + 12$​

Answer 1

Oie, Td Bom?!

$x {}^{4} - 7x {}^{2} + 12 = 0$

$x {}^{2 \: . \: 2} - 7x {}^{2} + 12 = 0$

$(x {}^{2} ) {}^{2} - 7x {}^{2} + 12 = 0$

• Substitua t = x².

$t {}^{2} - 7t + 12 = 0$

$t {}^{2} - 3t - 4t + 12 = 0$

$t \: . \: (t - 3) - 4(t - 3) = 0$

$(t - 3) \: . \: (t - 4) = 0$

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$t - 3 = 0⇒t = 3$

$t - 4 = 0⇒t = 4$

• Substitua x² = t.

$x {}^{2} = 3 ⇒x = ± \sqrt{3}$

$x {}^{2} = 4 ⇒x = ± \sqrt{4} ⇒x =±2$

• Solução:

$S = \left \{ - 2 \: , \: - \sqrt{3} \: , \: \sqrt{3} \: , \: 2\right \}$

Att. Makaveli1996