Question

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

Answer 1

xy = 1

Explanation:

Given

`x+y=(1)/(x)+(1)/(y)\\ \\x+y\\eq 0`

Simplify the first expression:

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