Question

three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

Answer 1

let the three numbers be x-1, x, x+1.
x^2 = (x-1)^2 - (x+1)^2
x^2 = x^2 +1 -2x -(x^2 +1+2x)
x^2 = x^2+1-2x-x^2 -1 -2x
x^2 = -4x
square rooting both sides
x =

Answer 2

hey mate......
here is your answer
x^2 = (x-1)^2 - (x+1)^2
x^2 = (x-1) (x-1) - (x+1) (x+1)
x^2 = x^2 - x - x -1 - x^2 + x+x+1
x^2 = 0