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ICSE Class 10 Answered

If q is mean proportion between p and r prove that p³+q³+r³/p²*q²*r²=1/l³+1/q³+1/r³
Asked by utkarshkumarcrick123 | 02 Feb, 2019, 12:02: AM
answered-by-expert Expert Answer
q is the mean proportional between p and r.
q2 = pr
begin mathsize 16px style LHS equals fraction numerator straight p cubed plus straight q cubed plus straight r cubed over denominator straight p squared straight q squared straight r squared end fraction equals fraction numerator begin display style straight p cubed plus straight q squared cross times pr plus straight r cubed end style over denominator begin display style straight p squared open parentheses pr close parentheses straight r squared end style end fraction equals fraction numerator begin display style straight p cubed plus straight q cross times pr plus straight r cubed end style over denominator begin display style straight p cubed straight r cubed end style end fraction space space space space space space space space space space space space space space space because straight q squared equals pr equals fraction numerator straight p cubed over denominator straight p cubed straight r cubed end fraction plus fraction numerator qpr over denominator straight p cubed straight r cubed end fraction plus fraction numerator straight r cubed over denominator straight p cubed straight r cubed end fraction equals fraction numerator begin display style 1 end style over denominator begin display style straight r cubed end style end fraction plus fraction numerator begin display style straight q end style over denominator begin display style straight p squared straight r squared end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight p cubed space end style end fraction space space space space space space space space space space space space space space space space equals fraction numerator begin display style 1 end style over denominator begin display style straight r cubed end style end fraction plus fraction numerator begin display style straight q end style over denominator begin display style open parentheses pr close parentheses open parentheses pr close parentheses end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight p cubed end style end fraction space space space space space space space space space space space because straight q squared equals pr space equals fraction numerator begin display style 1 end style over denominator begin display style straight r cubed end style end fraction plus fraction numerator begin display style straight q end style over denominator begin display style straight q squared straight q squared end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight p cubed end style end fraction space space space space space space space space space space space space space space space because straight q squared equals pr equals RHS equals fraction numerator begin display style 1 end style over denominator begin display style straight r cubed end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight q cubed end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight p cubed end style end fraction end style
Answered by Sneha shidid | 04 Feb, 2019, 10:22: AM

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