(√(x^2 +2))+(√(x^2 −4))=A (√(x^2 +2))−(√(x^2 −4))=?


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Question Number 183935 by SulaymonNorboyev last updated on 31/Dec/22

$\sqrt{x^{2} + 2} + \sqrt{x^{2} - 4} = A$ $\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} = ?$
	Answered by Rasheed.Sindhi last updated on 31/Dec/22
	$(√(x^2 +2))+(√(x^2 −4))=A (√(x^2 +2))−(√(x^2 −4))=? ((√(x^2 +2))+(√(x^2 −4)) )((√(x^2 +2)) −(√(x^2 −4)) ) =A((√(x^2 +2)) −(√(x^2 −4)) ) ((√(x^2 +2)) −(√(x^2 −4)) )=(1/A){(x^2 +2)−(x^2 −4)} (√(x^2 +2)) −(√(x^2 −4)) =(6/A)$
	$\sqrt{x^{2} + 2} + \sqrt{x^{2} - 4} = A$ $\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} = ?$ $(\sqrt{x^{2} + 2} + \sqrt{x^{2} - 4}) (\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4})$ $= A (\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4})$ $(\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4}) = \frac{1}{A} {(x^{2} + 2) - (x^{2} - 4)}$ $\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} = \frac{6}{A}$
	Commented by SulaymonNorboyev last updated on 31/Dec/22

	$T H A N K S Y O U$
	Answered by Rasheed.Sindhi last updated on 31/Dec/22

	$\sqrt{x^{2} + 2} + \sqrt{x^{2} - 4} = A$ $\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} = ?$ $a = \sqrt{x^{2} + 2}, b = \sqrt{x^{2} - 4}$ $a + b = A . . . . . . . . . (i)$ $a^{2} - b^{2} = (x^{2} + 2) - (x^{2} - 4) = 6$ $a - b = \frac{a^{2} - b^{2}}{a + b} = \frac{6}{A}$ $\sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} = \frac{6}{A}$
	Answered by manolex last updated on 31/Dec/22

	$m + n = A f i n d m - n$ $(m + n) (m - n) = (m - n) A$ $x^{2} + 2 - x^{2} + 4 = (m - n) A$ $\frac{6}{A} = \sqrt{x^{2} + 2} - \sqrt{x^{2} - 4} i s a n s w e r$
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