Q-8

If a,b,c are all non zero and a+b+c=0, prove that fraction numerator a squared over denominator b c end fraction plus fraction numerator begin display style b squared end style over denominator begin display style c a end style end fraction plus fraction numerator begin display style c squared end style over denominator begin display style a b end style end fraction equals 3

Asked by kishor.kp14 | 18th Jun, 2019, 10:00: AM

Expert Answer:

begin mathsize 16px style straight a squared over bc plus straight b squared over ca plus straight c squared over ab
equals fraction numerator straight a cubed plus straight b cubed plus straight c cubed over denominator abc end fraction
equals fraction numerator open parentheses straight a plus straight b plus straight c close parentheses begin display style open parentheses straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ca close parentheses end style begin display style plus end style begin display style 3 end style begin display style abc end style over denominator space abc end fraction space space space space because straight a cubed plus straight b cubed plus straight c cubed equals open parentheses straight a plus straight b plus straight c close parentheses open parentheses straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ca close parentheses plus 3 abc
equals fraction numerator 3 abc over denominator abc end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space because straight a plus straight b plus straight c equals 0
equals 3 end style

Answered by Sneha shidid | 18th Jun, 2019, 10:06: AM