#### Question

There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?

#### Solution

Let three consecutive integer be x , (x + 1)* *and (x + 2)

Then according to question

x2 + (x + 1)(x + 2) = 154

x2 + x2 + 3x + 2 = 154

2x2 - 3x + 2 - 154 = 0

2x2 + 3x - 152 = 0

2x2 - 16x - 19x - 152 = 0

2x(x - 8) + 19(x - 8) = 0

(x - 8)(2x + 19) = 0

(x - 8) = 0

x = 8

Or

2x + 19 = 0

2x = -19

x = -19/2

Since, *x *being a positive number, so *x* cannot be negative.

Therefore,

Whenx = 8then other positive integer

x + 1 = 8 + 1 = 9

And

x + 2 = 8 + 2 = 10

Thus, three consecutive positive integer be 8, 9, 10.

Is there an error in this question or solution?

#### APPEARS IN

Solution There Are Three Consecutive Integers Such that the Square of the First Increased by the Product of the First Increased by the Product of the Others the Two Gives 154. What Are the Integers? Concept: Solutions of Quadratic Equations by Factorization.