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ICSE Class 10 Answered

IF a, b, c ARE IN CONTINUED PROPORTION , PROVE THAT :- 1/a(cube)+1/b(cube)+1/c(cube)=a/b(square)c(square)+b/c(square)a(square)+c/a(square)b(square)
Asked by siddharthjaiswal1122 | 19 Aug, 2018, 05:14: PM
answered-by-expert Expert Answer
begin mathsize 18px style TPT colon space 1 over straight a cubed plus fraction numerator begin display style 1 end style over denominator begin display style straight b cubed end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight c cubed end style end fraction equals fraction numerator straight a over denominator straight b squared straight c squared end fraction plus fraction numerator begin display style straight b end style over denominator begin display style straight a squared straight c squared end style end fraction plus fraction numerator begin display style straight c end style over denominator begin display style straight a squared straight c squared end style end fraction let space straight a equals straight a comma space straight b equals ar comma space straight c equals ar squared fraction numerator begin display style 1 end style over denominator begin display style straight a cubed end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight b cubed end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight c cubed end style end fraction equals fraction numerator straight b cubed straight c cubed plus straight a cubed straight c cubed plus straight a cubed straight b cubed over denominator straight a cubed straight b cubed straight c cubed end fraction equals fraction numerator begin display style open parentheses ar cross times ar squared close parentheses cubed end style begin display style plus end style begin display style begin display style open parentheses straight a cross times ar squared close parentheses end style cubed end style begin display style plus end style begin display style begin display style open parentheses straight a cross times ar close parentheses end style cubed end style over denominator begin display style open parentheses straight a cross times ar cross times ar squared close parentheses cubed end style end fraction equals 1 over straight a cubed cross times fraction numerator begin display style open parentheses straight r close parentheses to the power of 9 plus open parentheses straight r close parentheses to the power of 6 plus open parentheses straight r close parentheses cubed end style over denominator begin display style open parentheses straight r close parentheses to the power of 9 end style end fraction equals open parentheses fraction numerator straight r cubed plus straight r squared plus 1 over denominator straight a cubed straight r to the power of 6 end fraction close parentheses fraction numerator begin display style straight a end style over denominator begin display style straight b squared straight c squared end style end fraction plus fraction numerator begin display style straight b end style over denominator begin display style straight a squared straight c squared end style end fraction plus fraction numerator begin display style straight c end style over denominator begin display style straight a squared straight c squared end style end fraction equals fraction numerator straight a cubed plus straight a cubed straight r cubed plus straight a cubed straight r cubed over denominator begin display style open parentheses straight a cubed straight r cubed close parentheses squared end style end fraction equals fraction numerator begin display style begin display style straight a end style cubed end style open parentheses 1 plus straight r cubed plus straight r to the power of 6 close parentheses over denominator straight a to the power of 6 open parentheses straight r to the power of 6 close parentheses end fraction equals open parentheses fraction numerator begin display style straight r cubed plus straight r squared plus 1 end style over denominator begin display style straight a cubed straight r to the power of 6 end style end fraction close parentheses end style
Answered by Arun | 20 Aug, 2018, 11:51: AM

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