Explanation Given information: Given, equation is x x + 3 − x + 3 x = 2 . Calculation: The equation can be written as: x x + 3 − 1 x x + 3 = 2 x x + 3 − 1 x x + 3 = 2 Substitute x x + 3 = y . y − 1 y = 2 y 2 y − 1 y = 2 y y y 2 − 1 = 2 y y 2 − 2 y − 1 = 0 The solutions to the quadratic equation of the form a x 2 + b x + c = 0 is given by x = − b ± b 2 − 4 a c 2 a . Here x = y , a = 1 , b = − 2 , c = − 1 Plugging the values in the above equation, we get, x = − b ± b 2 − 4 a c 2 a y = − ( − 2 ) ± ( − 2 ) 2 − 4 ( 1 ) ( − 1 ) 2 ( 1 ) y = 2 ± 4 + 4 2 y = 2 ± 8 2 y = 2 ± 2 2 2 y = 1 ± 1 2 1 y = 1 + 2 or y = 1 − 2 Substitute back the value of y to obtain the value of x. y = 1 + 2 or y = 1 − 2 x x + 3 = 1 + 2 or x x + 3 = 1 − 2 ( x x + 3 ) 2 = ( 1 + 2 ) 2 or ( x x + 3 ) 2 = ( 1 − 2 ) 2 x x + 3 = 1 + 2 2 + 2 or x x + 3 = 1 − 2 2 + 2 x x + 3 = 3 + 2 2 or x x + 3

Precalculus: A Unit Circle Approach (3rd Edition)

3rd Edition

ISBN: 9780134433042

Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek

Publisher: PEARSON

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Chapter A.6, Problem 46E

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To find the solution set of the given equation xx+3−x+3x=2.

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Chapter A.6, Problem 45E

Chapter A.6, Problem 47E

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Precalculus: A Unit Circle Approach (3rd Edition)

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To find the solution set of the given equation x x + 3 − x + 3 x = 2 .

Solution Summary: The author explains the solution set of the given equation, which is sqrtx+3-

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To find the solution set of the given equation xx+3−x+3x=2.

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Chapter A.6 Solutions