Question

Find two consecutive positive integer sum of whose square is 365

Answer 1

Answer is attached. ...

Verification :

(13)^2+(14)^2

=169+196

=365....Hence, verified

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Answer 2

Solution:

Let us say, the two consecutive positive integers be x and x + 1.

As per the given statement,

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.

So, x + 1 = 13 + 1 = 14

Therefore,

The two consecutive positive integers will be 13 and 14.