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

Quantitative Aptitude ( CCS) Number System

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

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Explanation:

Suppose the required number is x. Then from question,
x² + ( x + 3)² = 369 ⇔ x² + x² + 9 + 6x = 369
⇔ 2x² + 6x - 360 = 0 ⇔ x² + 3x - 180 = 0
⇔ ( x + 15) (x -12) = 0 ⇔ x = 12
So, The numbers are 12 and 15.
∴ Required sum = ( 12 + 15) = 27.