Explanation Given: The given equation is 3 x − x 3 − 12 ⋅ 3 x + 27 = 0 Calculation: Use the laws of exponent and simplify given equation. 3 2 x − 12 ⋅ 3 x + 27 = 0 ( 3 x ) 2 − 12 ⋅ 3 x + 27 = 0 [ ∵ ( a m ) n = a m n ] Substitute u for 3 x in above equation. ( u ) 2 − 12 ⋅ u + 27 = 0 u 2 − 12 u + 27 = 0 The above equation is a quadratic equation in u , split the middle term and solve the above equation. u 2 − 9 u − 3 u + 27 = 0 [ ∵ − 12 u = − 9 u − 3 u ] u ( u − 9 ) − 3 ( u − 9 ) = 0 [ Factor ] ( u − 9 ) ( u − 3 ) = 0 [ Factor u − 9 ] Use the zero product property and equate each factor to 0

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 5.1, Problem 25E

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The value of x in the equation 3x−x3−12⋅3x+27=0 .

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Chapter 5.1, Problem 24E

Chapter 5.1, Problem 26E

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Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - find the derivative of the function. 28...Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.5 - Prob. 48E Ch. 5.5 - Prob. 49E Ch. 5.5 - Prob. 50E Ch. 5.5 - Prob. 51E Ch. 5.5 - Prob. 52E Ch. 5.5 - Prob. 53E Ch. 5.5 - Prob. 54E Ch. 5.5 - Prob. 55E Ch. 5.5 - Prob. 56E Ch. 5.5 - Prob. 57E Ch. 5.5 - Prob. 58E Ch. 5.5 - Prob. 59E Ch. 5.5 - Prob. 60E Ch. 5.5 - Prob. 61E Ch. 5.5 - Prob. 62E Ch. 5.5 - Prob. 63E Ch. 5.5 - Prob. 64E Ch. 5.5 - Prob. 65E Ch. 5.5 - Prob. 66E Ch. 5.5 - Prob. 67E Ch. 5.5 - Prob. 68E Ch. 5.5 - Prob. 69E Ch. 5.5 - Prob. 70E Ch. 5.5 - Prob. 71E Ch. 5.5 - Prob. 72E Ch. 5.5 - 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The value of x in the equation 3 x − x 3 − 12 ⋅ 3 x + 27 = 0 .

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The value of x in the equation 3x−x3−12⋅3x+27=0 .

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Chapter 5 Solutions