Question

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

Answer 1

Answer :

$Now,\:xy [(x + y)(\frac{1}{x} + \frac{1}{y}) - 4]\\ \\ =xy [(x + y)(\frac{x+y}{xy})-4]\\ \\ =xy [\frac{(x+y)^{2}-4xy}{xy}]\\ \\ =(x+y)^{2} -4xy\\ \\ =x^{2} +y^{2}+2xy-4xy\\ \\ =x^{2}-2xy+y^{2}\\ \\ =(x-y)^{2}\\ \\ Hence, verified.$

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