Question

Find 2 consecutive positive integers ,sum of whose squares is 365​

Answer 1

Given:

Sum of whose is 365.

Find:

Two consecutive positive integer

Solution:

Let the conservative 1st position integer be x.

Let the conservative 2n position integer be x + 1.

we know that;

=> 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

=> x + 14 = 0 or x - 13 = 0

=> x = - 14 or x = 13

Since, the integers are positive, x can only be 13.

Therefore,

=> x + 1

=> 13 + 1

=> 14

Hence, the consecutive positive integer be 13 and 14.

I hope it will help you.

Regards.