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

Answer: Option A

Let the two number are a and b
According to question,
$$\begin{array}{rl}& a^2+b^2=289\\ & ab=120\\ & {\left(a+b\right)}^2=a^2+b^2+2ab\\ & {\left(a+b\right)}^2={\left(289\right)}^2+\left(2\times 120\right)\\ & {\left(a+b\right)}^2=529\\ & \left(a+b\right)=23\end{array}$$