Question

If x+y=1/x+1/y and x+y≠0, what is the value of xy?

Answer 1

Answer:

xy = 1

Step-by-step explanation:

Given

$x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0$

Simplify the first expression:

$x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}]$