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CBSE Class 8 Answered

if a : b = c : d then prove that   a^2 c + a c^2 : b^2 d + b d^2 = (a+c)^3 : (b+d)^3
Asked by Ramesh | 09 Feb, 2019, 10:04: PM
Expert Answer
begin mathsize 16px style straight a over straight b equals straight c over straight d equals straight k space left parenthesis say right parenthesis straight a equals bk comma space straight c equals dk.... left parenthesis straight i right parenthesis LHS equals fraction numerator straight a squared straight c plus ac squared over denominator straight b squared straight d plus bd squared end fraction equals fraction numerator ac open parentheses straight a plus straight c close parentheses over denominator bd open parentheses straight b plus straight d close parentheses end fraction equals fraction numerator begin display style bk cross times dk open parentheses bk plus dk close parentheses end style over denominator begin display style bd open parentheses straight b plus straight d close parentheses end style end fraction space space space space from space left parenthesis straight i right parenthesis equals fraction numerator straight k squared cross times straight k open parentheses straight b plus straight d close parentheses over denominator open parentheses straight b plus straight d close parentheses end fraction equals straight k cubed space space.... left parenthesis ii right parenthesis RHS equals fraction numerator begin display style open parentheses straight a plus straight c close parentheses cubed end style over denominator begin display style open parentheses straight b plus straight d close parentheses cubed end style end fraction equals open parentheses fraction numerator straight a plus straight c over denominator straight b plus straight d end fraction close parentheses cubed equals open parentheses fraction numerator begin display style bk plus dk end style over denominator begin display style straight b plus straight d end style end fraction close parentheses cubed equals open parentheses fraction numerator begin display style straight k open parentheses straight b plus straight d close parentheses end style over denominator begin display style straight b plus straight d end style end fraction close parentheses cubed equals straight k cubed space space..... left parenthesis iii right parenthesis Form space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis fraction numerator begin display style straight a squared straight c plus ac squared end style over denominator begin display style straight b squared straight d plus bd squared end style end fraction equals fraction numerator begin display style open parentheses straight a plus straight c close parentheses cubed end style over denominator begin display style open parentheses straight b plus straight d close parentheses cubed end style end fraction end style
Answered by Sneha shidid | 11 Feb, 2019, 09:44: AM

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