Question

The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is :

• A. 20
• B. 23
• C. 16
• D. None of these

Answer 1

The correct option is B 23

Let the number be $x$ and $y$

$\Rightarrow xy=120$

$\Rightarrow x^2+y^2=289$

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

$\Rightarrow {(x+y)}^2=289+2\times 120$

$\Rightarrow {(x+y)}^2=289+240$

$\Rightarrow {(x+y)}^2=529$

$\Rightarrow (x+y)=\sqrt{529}$

$=23.$

Hence, the answer is $23.$