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

A. 20

B. 23

C. 169

D. None of these

Solution:

Let the numbers be x and y
Then,
xy = 120 and x² + y² = 289

\begin{aligned} ∴ {(x + y)}^{2} \\ = x^{2} + y^{2} + 2 x y \\ = 289 + 240 \\ = 529 \\ ∴ x + y \\ = \sqrt{529} \\ = 23 \end{aligned}

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