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If x^2 - 4x + 1 = 0, what is x^2 + 1/x^2?

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If x^2 - 4x + 1 = 0, what is x^2 + 1/x^2?

by Max@Math Revolution » Thu Mar 12, 2020 12:18 am

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[GMAT math practice question]

If x^2 - 4x + 1 = 0, what is x^2 + 1/x^2?

A. 14
B. 16
C. 18
D. 20
E. 22
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Re: If x^2 - 4x + 1 = 0, what is x^2 + 1/x^2?

by Max@Math Revolution » Mon Mar 16, 2020 2:54 am
=>

x^2 - 4x + 1 = 0
x – 4 + 1/x = 0 (dividing both sides by x)
x + 1/x = 4 (adding 4 to both sides)
(x+1/x)^2 = 16 (squaring both sides)
x^2 +2x(1/x) + 1/x^2 = 16 (foiling the left side)
x^2 + 1/x^2 + 2 = 16 (simplifying)
x^2 + 1/x^2 = 14 (subtracting 2 from both sides)

Therefore, A is the answer.
Answer: A
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