3.Find two consecutive positive integers, sum of whose squares is 613.

1.	3.Find two consecutive positive integers, sum of whose squares is 613.
Answer» Let two consecutive positive integers be X, x + 1 according to the question x² + (x + 1)² = 613 x² + x² + 1 + 2x = 613 2x² + 2x = 613 - 1 2x² + 2x - 612 = 0 2 ( x² + x - 306 ) = 0 x² + x - 306 = 0 x² - 18x + 17x - 306 = 0 x (x - 18) + 17 (x - 18) = 0 (x - 18) (x + 17) = 0 x = 18 x = -17 thanks

Answer»

Let two consecutive positive integers be X, x + 1

according to the question

x² + (x + 1)² = 613

x² + x² + 1 + 2x = 613

2x² + 2x = 613 - 1

2x² + 2x - 612 = 0

2 ( x² + x - 306 ) = 0

x² + x - 306 = 0

x² - 18x + 17x - 306 = 0

x (x - 18) + 17 (x - 18) = 0

(x - 18) (x + 17) = 0

x = 18

x = -17

thanks

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