If-and-are-the-roots-of-of-the-equation-3x-2-x-3-0-find-thevalue-of-2-2-if-gt-

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

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