If `a ,b ,c`are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=( – InterviewSolution

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1.	If `a ,b ,c`are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)`
Answer» Let r be the common ratio of the given GP. Then, `b=ar and c=ar^(2)`. `:. LHS =(a^(2)+a^(2)r+a^(2)r^(2))/(a^(2)r+a^(2)r^(3)+a^(2)r^(2))=(a^(2)(1+r+r^(2)))/(a^(2)r(1+r+r^(2)))=1/r` `RHS=(ar+a)/(ar^(2)+ar)=(a(1+r))/(ar(1+r))=1/r`. Hence, `LHS=RHS`.

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