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4. Find two consecutive positive integers, sum of whose squares is 365.

4. Find two consecutive positive integers, sum of whose squares is 365.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
4 months ago
Let us say, the two consecutive positive integers be x and x + 1. Therefore, as per the given questions, x2 + (x + 1)2 = 365 ⇒ x2 + x2 + 1 + 2x = 365 ⇒ 2x2 + 2x – 364 = 0 ⇒ x2 + x – 182 = 0 ⇒ x2 + 14x – 13x – 182 = 0 ⇒ x(x + 14) -13(x + 14) = 0 ⇒ (x + 14)(x – 13) = 0 Thus, either, x + 14 = 0 or x – 13 = 0, ⇒ x = – 14 or x = 13 since, the integers are positive, so x can be 13, only. ∴ x + 1 = 13 + 1 = 14 Therefore, two consecutive positive integers will be 13 and 14.

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