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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For Problems 69 82 , find all real number solutions for each equation. (Objective 3)

8 x 2 32 = 0 .

To determine

To find:

All the real number solutions for the given problem.

Explanation

Approach:

i) The Difference of Two Squares pattern is a2b2=(a+b)(ab).

ii) Multiplication is commutative, so the order of writing the factors is not important. For example, (a+b)(ab) can also be written as (ab)(a+b).

iii) ab=0 if and only if a=0 or b=0.

The following steps have been followed to find out the solutions:

Step-1: Find out the common monomial factor and divide out from the equation.

Step-2: Convert the equation from step-1 in the form of 2 squares with subtraction and compare with the difference of two squares pattern.

Step-3: Apply the difference of two squares pattern to the equation available in step-2.

Step-4: Solve the equation and write the solutions set.

Calculation:

1) The given equation is 8x232=0.

The common monomial factor available in the above equation is 8.

So, the equation can be written as, 8(x24)=0.

Divide both sides of the equation by 8.

Therefore, x24=0.

2) The above equation can be written as,

x222=0

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