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Chapter 9: Q.464. (page 984)

Find two consecutive odd numbers whose product is323.

Short Answer

Expert verified

The pair of consecutive numbers are-17,-19and17,19.

Step by step solution

01

Step 1. Given information.

Two consecutive odd numbers whose product is23.

02

Step 2. Find two consecutive odd numbers.

Let the first odd number is x.

Then the second odd number is x+2.

Now, according to the question:

xx+2=323x2+2x=323x2+2x-323=0

03

Step 3. Solve the equation.

x2+2x-323=0x2+19x-17x-323=0xx+19-17x+19=0x+19x-17=0

04

Step 4. Apply zero product rule.

x+19=0x=-19and role="math" localid="1645768635050" x-17=0x=17

Hence, the first pair of consecutive numbers are -19and -19+2=-17.

The second pair of consecutive numbers are17and17+2=19.

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