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# Three Consecutive Positive Integers Are Such that the Sum of the Square of the First and the Product of Other Two is 46, Find the Integers. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.

#### Solution

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

Then according to question

x2 + (x + 1)(x + 2) = 46

x2 + x2 + 3x + 2 = 46

2x2 + 3x + 2 - 46 = 0

2x2 + 3x - 44 = 0

2x2 - 8x + 11x - 44 = 0

2x(x - 4) + 11(x - 4) = 0

(x - 4)(2x + 11) = 0

x - 4 = 0

x = 4

Or

2x + 11 = 0

2x = -11

x = -11/2

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

Therefore,

When x = 4 then other positive integer

x + 1 = 4 + 1 = 5

And

x + 2 = 4 + 2 = 6

Thus, three consecutive positive integer be 4, 5, 6.

Is there an error in this question or solution?

#### APPEARS IN

Solution Three Consecutive Positive Integers Are Such that the Sum of the Square of the First and the Product of Other Two is 46, Find the Integers. Concept: Solutions of Quadratic Equations by Factorization.
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