Question

Three consecutive positive integers are taken such that the sum of the square of the first and the product of the other two Is 154. Find the integers

Answer 1

Let the required three integers be (x-1), x and (x+1).

Now, (x-1)^2 + [x.(x+1)] = 154

(x^2-2x+1) + [x^2+x] = 154

2x^2 - x +1 = 154

2x^2 - x - 153 = 0

2x^2 - 18x + 17x - 153 = 0

2x(x-9) + 17(x-9) = 0

(x-9)(2x+17) = 0

x=9 or x=-17/2

So, x = 9 [because it is given that x is a positive integer]

.

Thus, the required integers are (9-1), 9 and (9+1), i.e. 8, 9 and 10.