Question

find two consecutive natural number whose the sum of square is 313

Answer 1

Let the numbers be x and x +1
According to the question
(x)^2 +(x+1)2 = 313
x^2+x^2+1+2x =313
2x^2+2x+1=313
2x^2+2x+1-313=0
2x^2+2x-312=0
x^2+x-156=0
x^2+13x-12x-156=0
x(x+13)-12(x+13)=0
(x-12)(x+13)=0
x-12=0
x=12
and
x+13=0
x= -13
Since x, being a natural number cannot be negative.
Therefore => x = 12
=> x+1 = 12+1 =13