If α and β are the roots of of the equation 3x^2 −x−3=0, find thevalue of (α^2 −β^2 ) if α>β.


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Question Number 56904 by pete last updated on 26/Mar/19

$If α and β are the roots of of the equation$ ${3 x}^{2} - x - 3 = 0, find thevalue of (α^{2} - β^{2})$ $if α > β .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 26/Mar/19

	${(α - β)}^{2} = {(α + β)}^{2} - 4 α β$ $α + β = \frac{- b}{a} = \frac{- (- 1)}{3} = \frac{1}{3}$ $α β = \frac{c}{a} = \frac{- 3}{3} = - 1$ ${(α - β)}^{2} = {(α + β)}^{2} - 4 α β$ $= \frac{1}{9} + 4 = \frac{37}{9}$ $(α - β) = \frac{\sqrt{37}}{3}$ $α^{2} - β^{2} = (α + β) (α - β)$ $= \frac{1}{3} \times \frac{\sqrt{37}}{3} = \frac{\sqrt{37}}{9}$
	Commented by pete last updated on 26/Mar/19

	$Thanks for your help .$
	Commented by tanmay.chaudhury50@gmail.com last updated on 26/Mar/19

	$m o s t w e l c o m e . . .$
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