Without using table, find the values of: (1/((1−(√3))^2 )) − (1/((1+(√3))^2 )) Mastermind


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Question Number 180837 by Mastermind last updated on 17/Nov/22

$Without using table, find the values$ $of :$ $\frac{1}{{(1 - \sqrt{3})}^{2}} - \frac{1}{{(1 + \sqrt{3})}^{2}}$ $Mastermind$
	Answered by Rasheed.Sindhi last updated on 18/Nov/22
	$(1/((1−(√3))^2 )) − (1/((1+(√3))^2 )) (((1+(√3))^2 −(1−(√3))^2 )/((1−(√3))^2 (1+(√3))^2 )) (({(1+(√3) )−(1−(√3) )}{(1+(√3) )+(1−(√3) )})/({(1)^2 −((√3) )^2 }^2 )) (((1+(√3) −1+(√3) )(1+(√3) +1−(√3) ))/((1−3)^2 )) (((2(√3) )(2))/2^2 ) =(√3)$
	$\frac{1}{{(1 - \sqrt{3})}^{2}} - \frac{1}{{(1 + \sqrt{3})}^{2}}$ $\frac{{(1 + \sqrt{3})}^{2} - {(1 - \sqrt{3})}^{2}}{{(1 - \sqrt{3})}^{2} {(1 + \sqrt{3})}^{2}}$ $\frac{{(1 + \sqrt{3}) - (1 - \sqrt{3})} {(1 + \sqrt{3}) + (1 - \sqrt{3})}}{{{(1)}^{2} - {(\sqrt{3})}^{2}}^{2}}$ $\frac{(1 + \sqrt{3} - 1 + \sqrt{3}) (1 + \sqrt{3} + 1 - \sqrt{3})}{{(1 - 3)}^{2}}$ $\frac{(2 \sqrt{3}) (2)}{2^{2}}$ $= \sqrt{3}$
	Answered by Socracious last updated on 19/Nov/22

	$\sqrt{3}$
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