Question

If $a-b=2$ and $ab=48$, find the value of $a^2+b^2$.

• A. $50$
• B. $100$
• C. $150$
• D. $0$

Answer 1

The correct option is B

$100$

Consider the identity $(a-b{)}^2=a^2+b^2-2ab$

Re-arranging the equation, $a^2+b^2=(a-b{)}^2+2ab$

Given $a-b=2$ and $ab=48$

So, by substitution, $a^2+b^2=(2{)}^2+2(48)=4+96=100$