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Intermediate Algebra

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

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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)

x 4 81 = 0 .

To determine

To find:

All the real number solutions for the given equation.

Explanation

Approach:

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

ii) Polynomial in the form of The Sum of Two Squares pattern like a2+b2 is not factorable using integers.

iii) 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).

iv) abc=0 if and only if a=0 or b=0 or c=0.

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

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

Step-2: Apply the difference of two squares pattern to the equation available in step-1.

Step-3: If the equations are in the sum of two squares pattern and the difference of two squares pattern, then solve the sum of two squares pattern. For the difference of two squares pattern, do the step-1 and step-2 again, and write the solutions set.

Calculation:

1) The given equation is x481=0.

It can be written as,

x434=0(x2)2(32)2=0

Because, (x2)2=x2x2=x2+2=x4 and 34=3232=3333=81.

Since the above equation has 2 squares and they are subtracted, it represents the difference of two squares pattern. That is, a2b2=(a+b)(ab).

2) Now, we can apply the difference of two squares pattern to the above equation

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