Question

The sum of two numbers is equal to the sum of their reciprocals. What will be the product of the numbers?

• A. $5$
• B. $6$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $1$

x + y = $\frac{1}{x}+\frac{1}{y}\Rightarrow x+y=\frac{y+x}{xy}$
$\Rightarrow xy=\frac{y+x}{x+y}=1$