Q4: Find two consecutive positive integers, sum of whose squares is 365.

Q4: Find two consecutive positive integers, sum of whose squares is 365.

Answer:

 Let first number = x

Then second number will one more so that next number wil x+1

Given that sum of whose squares is 365.

      x²+ (  x + 1)² = 365

use formula of (a +b)² = a² + 2ab +b²

    x²+   x²+ 2x + 1 – 365 = 0

  2x²+ 2x – 364 = 0

Divide by 2 to simplify it

    x²+   x – 182 = 0

factorize it now

Therefore required numbers are 13 and 14