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If G be the the geometric mean of x and y then 1/G^2-x^2 +1/G^2-y^2? If G be the the geometric mean of x and y then 1/G^2-x^2 +1/G^2-y^2?
G^2 = XY SO 1/(G²-x²)+1/(G²-y²) = 1/(XY-X^2) + 1/(XY-Y^2) = 1/X* 1/(Y-X)+1/Y* 1/(X-Y) = 1/(x-y)[1/y - 1/x] =1/(x-y) *[(x-y)/xy] = 1 / xy = 1 / G^2
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