SOLUTION: If x^2+y^2=10xy, prove that 2 log ( x+y/x-y)=log 3/2

Question 777869: If x^2+y^2=10xy, prove that 2 log ( x+y/x-y)=log 3/2
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x^2+y^2=10xy
x^2+2xy+y^2=10xy+2xy
(x+y)^2= 10xy+2xy
(x+y)^2=12xy
x^2+y^2=10xy
x^2-2xy+y^2=10xy-2xy
(x-y)^2=8xy

2 log ( x+y/x-y)=log 3/2
LHS
2 log ( x+y/x-y)
log((x+y)/(x-y))^2
=log((x+y)^2/(x-y)^2)
=log (12xy/8xy)
= log3/2=RHS
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