If a, b, c are distinct real numbers such that a squared space minus space b space equals space b squared space minus space c space equals space c squared space minus space a space t h e n comma space f i n d space left parenthesis a space plus b right parenthesis left parenthesis b plus c right parenthesis left parenthesis c plus a right parenthesis

Asked by a.behera67 | 4th Jan, 2016, 09:07: PM

Expert Answer:

straight a squared minus straight b equals straight b squared minus straight c straight a squared minus straight b squared equals straight b minus straight c left parenthesis straight a minus straight b right parenthesis left parenthesis straight a plus straight b right parenthesis equals left parenthesis straight b minus straight c right parenthesis left parenthesis straight a plus straight b right parenthesis equals fraction numerator left parenthesis straight b minus straight c right parenthesis over denominator left parenthesis straight a minus straight b right parenthesis end fraction.................... left parenthesis 1 right parenthesis  straight b squared minus straight c equals straight c squared minus straight a straight b squared minus straight c squared equals straight c minus straight a left parenthesis straight b minus straight c right parenthesis left parenthesis straight b plus straight c right parenthesis equals left parenthesis straight c minus straight a right parenthesis left parenthesis straight b plus straight c right parenthesis equals fraction numerator left parenthesis straight c minus straight a right parenthesis over denominator left parenthesis straight b minus straight c right parenthesis end fraction.................... left parenthesis 2 right parenthesis  straight a squared minus straight b equals straight c squared minus straight a straight a squared minus straight c squared equals straight b minus straight a left parenthesis straight a minus straight c right parenthesis left parenthesis straight a plus straight c right parenthesis equals left parenthesis straight b minus straight a right parenthesis left parenthesis straight a plus straight c right parenthesis equals fraction numerator left parenthesis straight b minus straight a right parenthesis over denominator left parenthesis straight a minus straight c right parenthesis end fraction.................... left parenthesis 3 right parenthesis  LHS space equals space left parenthesis straight a plus straight b right parenthesis left parenthesis straight b plus straight c right parenthesis left parenthesis straight c plus straight a right parenthesis equals fraction numerator left parenthesis straight b minus straight c right parenthesis over denominator left parenthesis straight a minus straight b right parenthesis end fraction cross times fraction numerator left parenthesis straight c minus straight a right parenthesis over denominator left parenthesis straight b minus straight c right parenthesis end fraction cross times fraction numerator left parenthesis straight b minus straight a right parenthesis over denominator left parenthesis straight a minus straight c right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space left square bracket from space left parenthesis 1 right parenthesis comma space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis right square bracket equals 1

Answered by Vijaykumar Wani | 5th Jan, 2016, 11:46: AM