Question

three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the Other 2 by 60 find the number

Answer 1

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Answer 2

let three consecutive numbers be x,x+1,x+2
by given condition
(x+1)^2 = x^2 - (x+2)^2 + 60
x^2+ 2x + 1 =x^2 -( x^2+4x+4)+60
x^2+2x+1 = - (4x+4)+60
x^2+6x+5--60=0
x^2 + 6x -- 55=0
(x+11)(x- 5)=0
so x= --11 or x=5
but x is natural number
so x= 5
so three consecutive natural number are
5,6,7