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Chapter 6: Q. 460 (page 638)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Assume the integers.

Assume the first integer to be xand 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" xx+1=156x2+x=156

Bring all the terms to one side,

role="math" localid="1644850766182" x2+x-156=0

02

Step 2. Factor the equation.

On factoring,

x2+13x-12x-156=0xx+13-12x+13=0x+13x-12=0

Then,

x+13=0x=-13

Also,

x-12=0x=12

03

Step 3. Find the two integers.

When x=-13then the other consecutive number,

x+1=-13+1=-12

When x=12then the other consecutive number,

x+1=12+1=13

04

Step 4. Check the answers.

Substitute -13,-12in the original equation,

-13脳-12=156156=156

This is true.

Substitute 12,13in the original equation,

12脳13=156156=156

This is also true.

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