Question

If the sum of two numbers a and b is 10 and sum of their squares is 52, then the product of a and b is _____.

• A. 23
• B. 53
• C. 24
• D. 62

Answer 1

The correct option is C 24

$a+b=10\text{and}{a}^2+b^2=52$
$2ab=(a+b{)}^2-(a^2+b^2)$ $[\because (a+b{)}^2=a^2+b^2+2ab]$
$\Rightarrow 2ab=(10{)}^2-52=100-52=48$
$ab=\frac{1}{2}\times 48=24$