solve: (√(x^2 +5x+2)) −(√(x^2 +5 )) =1


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Question Number 172006 by Mikenice last updated on 23/Jun/22

$s o l v e :$ $\sqrt{x^{2} + 5 x + 2} - \sqrt{x^{2} + 5} = 1$
	Answered by Rasheed.Sindhi last updated on 24/Jun/22

	$\sqrt{x^{2} + 5 x + 2} - \sqrt{x^{2} + 5} = 1$ $\sqrt{x^{2} + 5 x + 2} = 1 + \sqrt{x^{2} + 5}$ $x^{2} + 5 x + 2 = 1 + x^{2} + 5 + 2 \sqrt{x^{2} + 5}$ $5 x - 3 = 2 \sqrt{x^{2} + 5}$ $25 x^{2} - 30 x + 9 = 4 x^{2} + 20$ $21 x^{2} - 30 x - 11 = 0$ $x = \frac{30 \pm \sqrt{900 + 924}}{42} = \frac{30 \pm 4 \sqrt{114}}{42}$ $= \frac{15 \pm 2 \sqrt{114}}{21}$ $A n s w e r s s h o u l d b e t e s t e d f o r v a l i d i t y .$
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