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1. The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is :

A. 25

B. 27

C. 33

D. 81

Solution:

Let the numbers be x and (x + 3)
Then,

\begin{aligned} \Leftrightarrow x^{2} + {(x + 3)}^{2} = 369 \\ \Leftrightarrow x^{2} + x^{2} + 9 + 6 x = 369 \\ \Leftrightarrow 2 x^{2} + 6 x - 360 = 0 \\ \Leftrightarrow x^{2} + 3 x - 180 = 0 \\ \Leftrightarrow (x + 15) (x - 12) = 0 \\ \Leftrightarrow x = 12 \end{aligned}

So, the numbers are 12 and 15
∴ Required sum = (12 + 15) = 27

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