Explanation The given equation is 3 x 2 − 2 − x 2 + 7 = 1 . Isolate the radical by adding x 2 + 7 from both sides of the equation as follows. 3 x 2 − 2 − x 2 + 7 + x 2 + 7 = 1 + x 2 + 7 3 x 2 − 2 = 1 + x 2 + 7 Take square on both sides and simplify as follows. ( 3 x 2 − 2 ) 2 = ( 1 + x 2 + 7 ) 2 3 x 2 − 2 = 1 + x 2 + 7 + 2 x 2 + 7 2 x 2 − 10 = 2 x 2 + 7 x 2 − 5 = x 2 + 7 On further simplification, ( x 2 − 5 ) 2 = ( x 2 + 7 ) 2 x 4 + 25 − 10 x 2 = x 2 + 7 x 4 − 10 x 2 + 18 = 0 y 2 − 10 y + 18 = 0 [ Let y = x 2 ] On further simplification, ( y − 9 ) ( y − 2 ) = 0 y − 9 = 0 or y − 2 = 0 y = 9 or y = 2 x 2 = 9 or x 2 = 2 [ ∵ y = x 2 ] x = ± 3 or x = ± 2 Thus, the solution of the equation is x = ± 3 and x = ± 2 _ . Check the solution by substituting x = 3 in 3 x 2 − 2 − x 2 + 7 = 1

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Author: Allyn Washington, Richard Evans

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Chapter 14, Problem 44RE

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Chapter 14, Problem 43RE

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Chapter 14 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 14.1 - In Example 7, determine how many times the rocket...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E

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The equation 3 x 2 − 2 − x 2 + 7 = 1 .

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