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Chapter 10: Q 287. (page 1237)

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

Find two consecutive odd numbers whose product is 323.

Short Answer

Expert verified

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

Step by step solution

01

Given information.

The given statement is:

Find two consecutive odd numbers whose product is 323.

02

Setup an equation so that the product of two consecutive odd numbers is 323.

Let the first odd number be x.

So, the next odd number bex+2.

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

03

Solve for the value of x.

Factor the left side of the equation as x+19x-17=0

Now apply the zero product property.

x+19=0x=-19Andx-17=0x=17

So, the first pair of consecutive numbers are-19and-19+2=-17.The second pair of consecutive numbers are17and17+2=19.

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