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CBSE Class 9 Answered

iF a+b+c = 0, then prove that (b+c)2 / 3bc  + (c+a)2 / 3ca  +  (a+b)2 / 3ab = 1
Asked by Vikas | 05 Mar, 2018, 12:04: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight a plus straight b plus straight c equals 0 rightwards double arrow straight a plus straight b equals negative straight c comma space space space straight b plus straight c equals negative straight a comma space space space space space straight c plus straight a equals negative straight b Now comma fraction numerator left parenthesis straight b plus straight c right parenthesis squared over denominator 3 bc end fraction plus fraction numerator left parenthesis straight c plus straight a right parenthesis squared over denominator 3 ca end fraction plus fraction numerator left parenthesis straight a plus straight b right parenthesis squared over denominator 3 ab end fraction equals fraction numerator left parenthesis negative straight a right parenthesis squared over denominator 3 bc end fraction plus fraction numerator left parenthesis negative straight b right parenthesis squared over denominator 3 ca end fraction plus fraction numerator left parenthesis negative straight c right parenthesis squared over denominator 3 ab end fraction equals fraction numerator straight a squared over denominator 3 bc end fraction plus fraction numerator straight b squared over denominator 3 ca end fraction plus fraction numerator straight c squared over denominator 3 ab end fraction equals fraction numerator straight a cubed plus straight b cubed plus straight c cubed over denominator 3 abc end fraction equals fraction numerator 3 abc over denominator 3 abc end fraction space space space space space space space left square bracket since space straight a plus straight b plus straight c equals 0 rightwards double arrow straight a cubed plus straight b cubed plus straight c cubed equals 3 abc right square bracket equals 1 end style
Answered by Rashmi Khot | 05 Mar, 2018, 02:37: PM

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