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Chapter 9: Q. 9.70 (page 910)

The product of two consecutive even integers is 168. Find the integers.

Short Answer

Expert verified

Two consecutive even integers whose product is 168 are 12, 14 and -12,-14.

Step by step solution

01

Step 1. Form a quadratic equation.

It is given that the product of two consecutive even integers is 168.

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

n(n+2)=168n2+2n-168=0

02

Step 2. Solve the equation.

Split the middle term.

n2+14n-12n-168=0n(n+14)-12(n+14)=0(n-12)(n+14)=0n=12andn=-14

03

Step 3. Determine the second even integer.

For n=12,

n+2=12+2=14

For n=-14,

n+2=-14+2=-12

04

Step 4. Conclusion.

Two consecutive even integers whose product is 168 are 12, 14 and -12,-14.

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