Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.1 - Ratios, Rates, and Proportions - Exercises - Page 226: 14b

Answer

X ≢ ℝ (All Real Numbers) X $\ne$ 0 X $\ne$ 2

Work Step by Step

(X+2) x (X-2) = 2X^2 (X+2) x (x-2) - 2x^2 = 0 X^2 - 4 - 2X^2 -X^2 - 4 = 0 X^2 = 4 X = + or - $\sqrt-4$ X ≢ ℝ (All Real Numbers) X $\ne$ 0 X $\ne$ 2 1. Move variable to the left side and change its sign. 2. Using (a-b)(a+b)= a^2-b^2, simplify the product. 3. Collect like terms. 4. Move constant to the right side and change its sign. 5. Change the signs on both sides of the equation. 6. Square root both sides of the equation. 7. The square root of a negative number does not exist in the set of Real Numbers. 8. Exclude the solution equal to any restricted value of x. (X $\ne$ ℝ)
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