Question

Verify that xy[(x+y)(1/x+1/y) -4] = ( x-y)²

Answer 1

Taking L.H.S.
=xy[(x+y)(x+y/xy)-4]
=xy[(x+y)^2-4xy]/xy
=(x+y)^2 -4xy
=x^2 +y^2 +2xy-4xy
=x^+y^2 -2xy
=(x-y)^2
=R.H.S.
Hence proved.