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Chapter 9: Q. 9.69 (page 909)

The product of two consecutive odd integers is 99. Find the integers.

Short Answer

Expert verified

Two consecutive odd integers whose product is 99 are 9, 11 and -9,-11.

Step by step solution

01

Step 1. Form a quadratic equation.

It is given that the product of two consecutive odd integers is 99.

Let nbe the first odd integer and n+2is the second odd integer. Then,

n(n+2)=99n2+2n-99=0

02

Step 2. Solve the equation.

Split the middle term.

n2+11n-9n-99=0n(n+11)-9(n+11)=0(n-9)(n+11)=0n=9andn=-11

03

Step 3. Determine the second odd integer.

For n=9,

n+2=9+2=11

Forn=-11

n+2=-11+2=-9

04

Step 4. Conclusion.

Two consecutive odd integers whose product is 99 are 9, 11 and -9,-11.

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