Explanation The given equation is 4 r 2 + 1 + 7 2 r 2 + 1 = 2 . In order to find the value of x , first rewrite the equation in quadratic form. Multiply on both sides by ( 2 r 2 + 1 ) ( r 2 + 1 ) and simplify the equation as follows. 4 r 2 + 1 ( 2 r 2 + 1 ) ( r 2 + 1 ) + 7 2 r 2 + 1 ( 2 r 2 + 1 ) ( r 2 + 1 ) = 2 ( 2 r 2 + 1 ) ( r 2 + 1 ) 4 ( 2 r 2 + 1 ) + 7 ( r 2 + 1 ) = 2 ( 2 r 4 + 3 r 2 + 1 ) 8 r 2 + 4 + 7 r 2 + 1 = 4 r 4 + 6 r 2 + 2 4 r 4 − 9 r 2 − 9 = 0 Substitute y = t 2 in 4 r 4 − 9 r 2 − 9 = 0 and simplify the equation as follows. 4 y 2 − 9 y − 9 = 0 ( 4 y + 3 ) ( y − 3 ) = 0 4 y + 3 = 0 or y − 3 = 0 4 y = − 3 or y = 3 On further simplification, t 2 = − 3 4 or t 2 = 3 [ ∵ y = t 2 ] t = ± j 3 2 or t = ± 3 Thus, the solution of the equation is t = ± j 3 2 or t = ± 3 . Check the solution by substituting x = j 3 2 in 4 r 2 + 1 + 7 2 r 2 + 1 = 2 . 4 ( j 3 2 ) 2 + 1 + 7 2 ( j 3 2 ) 2 + 1 = ? 2 4 − 3 4 + 1 + 7 2 ( − 3 4 ) + 1 = ? 2 4 ⋅ ( 4 1 ) + 7 − 1 2 = ? 2 16 − 14 = ? 2 2 = ? 2 [ True ] Check the solution by substituting x = − j 3 2 in 4 r 2 + 1 + 7 2 r 2 + 1 = 2

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ISBN: 9780134437705

Author: Washington

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Chapter 14, Problem 37RE

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To solve: The equation 4r2+1+72r2+1=2.

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Chapter 14, Problem 36RE

Chapter 14, Problem 38RE

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The equation 4 r 2 + 1 + 7 2 r 2 + 1 = 2 .

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To solve: The equation 4r2+1+72r2+1=2.

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Chapter 14 Solutions