solve: x(√(x^2 +4)) −x^2 =−6


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Question Number 172007 by Mikenice last updated on 23/Jun/22

$s o l v e :$ $x \sqrt{x^{2} + 4} - x^{2} = - 6$
	Answered by puissant last updated on 23/Jun/22
	$x(√(x^2 +4)) = x^2 −6 ⇒ x^2 (x^2 +4)=x^4 −12x^2 +36 ⇒ x^4 +4x^2 =x^4 −12x^2 +36 ⇒ 16x^2 −36=0 ⇒ (4x)^2 −6^2 =0 ⇒ 4x=6 or 4x=−6 ⇒ x=(3/2) or x=−(2/3) S={−(2/3) ; (2/3) }$
	$x \sqrt{x^{2} + 4} = x^{2} - 6$ $\Rightarrow x^{2} (x^{2} + 4) = x^{4} - 12 x^{2} + 36$ $\Rightarrow x^{4} + 4 x^{2} = x^{4} - 12 x^{2} + 36$ $\Rightarrow 16 x^{2} - 36 = 0$ $\Rightarrow {(4 x)}^{2} - 6^{2} = 0$ $\Rightarrow 4 x = 6 o r 4 x = - 6$ $\Rightarrow x = \frac{3}{2} o r x = - \frac{2}{3}$ $S = {- \frac{2}{3}; \frac{2}{3}}$
	Commented by Mikenice last updated on 23/Jun/22

	$p l e a s e s i r r e c h e c k y o u r s o l u t i o n$
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