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Question

If x2+y225xy, then prove 2log(x+y)=3 log 3+log x+log y

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Solution


x2+y2=25xy x2+y2+2xy=25xy+2xy (Adding 2xy on both sides) (x+y)2=27xy log(x+y)2=log 27xy (taking log on both sides) 2 log(x+y)=log27+log x+log y (log abc=log a+log b+log c) 2log(x+y)=log 33+logx+logy 2log(x+y)=3log3+logx+logy

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