Explanation Given Information: The equation is x 4 − 13 x 2 + 36 = 0 . Formula used: Principle of square roots: If x 2 = k , then x = k or x = − k , where k is any real number. Calculation: Consider the equation. x 4 − 13 x 2 + 36 = 0 ………… (1) The value of x in the equation x 4 − 13 x 2 + 36 = 0 is calculated as follows. Consider u = x 2 then u 2 = x 4 . Substitute u for x 2 in the equation (1). x 4 − 13 x 2 + 36 = 0 u 2 − 13 u + 36 = 0 u 2 − 4 u − 9 u + 36 = 0 u ( u − 4 ) − 9 ( u − 4 ) = 0 Simplify further as follows. ( u − 4 ) ( u − 9 ) = 0 Use zero factor. u − 4 = 0 u = 4 Or, u − 9 = 0 u = 9 Substitute u = x 2 and apply square root property

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Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 12, Problem 11CR

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Chapter 12, Problem 10CR

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The value of x from the equation x 4 − 13 x 2 + 36 = 0 .

Solution Summary: The author explains how to calculate the value of x in the equation x432+36=0.

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