Explanation Property Used: Zero-Product Property: If a b = 0 , then a = 0 or b = 0 . Procedure Used: Solving a Radical Equation Containing Two Radicals : Step 1: Isolate one of the radicals. That is, get one of the radicals by itself on one side of the equation. Step 2: Raise both sides of the equation to the power of the index. This will eliminate one or both radicals from the equation. Step 3: If a radical remains in the equation, then follow the steps for solving a radical equation containing one radical. Otherwise, solve the equation that results. Step 4: Check your answer. Discard any extraneous solutions. Calculation: The given equation is, 2 x − 1 − x − 1 = 1 can be written as, 2 x − 1 − x − 1 + x − 1 = 1 + x − 1 ( Add x − 1 on both sides ) 2 x − 1 = 1 + x − 1 Squaring on both sides of the given equation and simplify as, ( 2 x − 1 ) 2 = ( 1 + x − 1 ) 2 2 x − 1 = 1 + 2 x − 1 + ( x − 1 ) 2 ( Using ( A + B ) 2 = A 2 + 2 A B + B 2 ) 2 x − 1 = 1 + 2 x − 1 + x − 1 2 x − 1 = 2 x − 1 + x Isolate the radical as follows. 2 x − 1 − x = 2 x − 1 + x − x ( Subtract x from both sides ) x − 1 = 2 x − 1 Raise both sides of the equation to the power of the index. ( x − 1 ) 2 = ( 2 x − 1 ) 2 ( Squaring on both sides ) x 2 − 2 x + 1 = 4 ( x − 1 ) x 2 − 2 x + 1 = 4 x − 4 x 2 − 2 x + 1 − 4 x = 4 x − 4 − 4 x ( Subtract 4 x from both sides ) Solve further as,

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 9.8, Problem 54E

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To solve: The equation 2x−1−x−1=1.

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Chapter 9.8, Problem 53E

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The equation 2 x − 1 − x − 1 = 1 .

Solution Summary: The author explains the procedure for solving a radical equation containing two radicals.

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