Question

The difference between two positive numbers is $5$ and the sum of their squares is $73$. Find the product of these numbers.

• A. $24$
• B. $22$
• C. $16$
• D. $32$

Answer 1

The correct option is A $24$

Let the two number be $x$ and $y$
Therefore,
$x-y=5$ and $x^2+y^2=73$
Now,
$(x-y{)}^2=x^2+y^2-2xy$
$=>(5{)}^2=73-2xy$
$=>25=73-2xy$
$=>2xy=73-25$
$=>xy=\frac{48}{2}$
$=>xy=24$
Therefore, product of $xy$ is $24$.