Question

If $x+y=\sqrt{22}$ and $x-y=\sqrt{10}$, then $xy=$

• A. $\sqrt{22\times 10}$
• B. $3$
• C. $12$
• D. $55$
• E. $16$

Answer 1

The correct option is B $3$

Squaring both sides of the given equations as follows:

$(x+y{)}^2=22$ and $(x-y{)}^2=10$

$x^2+y^2+2xy=22$ and $x^2+y^2-2xy=10$

Subtracting the equations, we get

$(x^2+y^2+2xy)-(x^2+y^2-2xy)=22-10$

This implies $4xy=12$

$\therefore xy=3$

Hence option $B$ is correct.