Question

There are two numbers such that their product is 12 and the sum of the numbers is 8.

Find the sum of their squares.

• A. 40
• B. 52
• C. 4
• D. 22

Answer 1

The correct option is A

40

Let the numbers be x and y.

Given: $xy=12,(x+y)=8$

$\Rightarrow (x+y{)}^2=x^2+y^2+2xy$

$\Rightarrow (8{)}^2=(x^2+y^2)+2(12)$

$\Rightarrow (x^2+y^2)=(8{)}^2-2(12)=64-24=40$