Chapter 6: Q. 460 (page 638)

The product of two consecutive integers is $156$ . Find the integers.

Short Answer

Expert verified

The two required integers are $\{- 13, - 12\}, {12, 13}$ .

Step by step solution

Step 1. Assume the integers.

Assume the first integer to be $x$ and the other consecutive integer to be $x + 1$ .

From the given question,

The product of two consecutive integers is $156$ . Then,

role="math" localid="1644850745312" $x (x + 1) = 156 x^{2} + x = 156$

Bring all the terms to one side,

role="math" localid="1644850766182" $x^{2} + x - 156 = 0$

Step 2. Factor the equation.

On factoring,

$x^{2} + 13 x - 12 x - 156 = 0 x (x + 13) - 12 (x + 13) = 0 (x + 13) (x - 12) = 0$

Then,

$x + 13 = 0 x = - 13$

Also,

$x - 12 = 0 x = 12$

Step 3. Find the two integers.

When $x = - 13$ then the other consecutive number,

$x + 1 = - 13 + 1 = - 12$

When $x = 12$ then the other consecutive number,

$x + 1 = 12 + 1 = 13$

Step 4. Check the answers.

Substitute $- 13, - 12$ in the original equation,

$(- 13) \times (- 12) = 156 156 = 156$

This is true.

Substitute $12, 13$ in the original equation,

$12 \times 13 = 156 156 = 156$

This is also true.

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The product of two consecutive integers is $156$ . Find the integers.

Short Answer

Step by step solution

Step 1. Assume the integers.

Step 2. Factor the equation.

Step 3. Find the two integers.

Step 4. Check the answers.

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The product of two consecutive integers is156. Find the integers.

Short Answer

Step by step solution

Step 1. Assume the integers.

Step 2. Factor the equation.

Step 3. Find the two integers.

Step 4. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Pure Maths

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The product of two consecutive integers is $156$ . Find the integers.