Answer to Question #4919 in Algebra for jojo alex

Question

the sum of the squares of 2 consecutive natural numbers is 313 find the number

Answer 1

Let first positive integer is x. second is (x+1).

x^2 +(x+1)^2 = 313
x^2 + x^2 + 2x + 1 = 313
2x^2 + 2x - 312 = 0
x^2 + x - 156 = 0
x^2 + 13x - 12x - 156 = 0
x(x+13) - 12(x+13) = 0
(x+13)(x-12) = 0
x = -13 or x = 12
x =-13 rejected,
x = 12, and x+1 = 12+1 = 13

So, two consecutive positive integers are 12 and 13.