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x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

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x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?  [#permalink]

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New post 01 May 2019, 00:49
4
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (02:00) correct 44% (02:48) wrong based on 43 sessions

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[GMAT math practice question]

\(x^2 + 4x + 1 = 0\). What is the value of \(x^2 + \frac{1}{x^2}\)?

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)

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Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?  [#permalink]

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New post 01 May 2019, 01:07
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MathRevolution wrote:
[GMAT math practice question]

\(x^2 + 4x + 1 = 0\). What is the value of \(x^2 + \frac{1}{x^2}\)?

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)


i.e. \(x^2 + 4x + 1 = 0\)

Dividing both sides by x we get

i.e. \(x + 4 + \frac{1}{x} = 0\)

i.e. \(x + \frac{1}{x} = -4\)

Squaring both sides we get

\(x^2 + \frac{1}{x^2}+2*x*\frac{1}{x} = 16\)

i.e. \(x^2 + \frac{1}{x^2} = 14\)

Answer: Option C
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Math Revolution GMAT Instructor
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Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?  [#permalink]

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New post 03 May 2019, 00:16
=>

\(x^2 + 4x + 1 = 0\)

\(=> x + 4 + \frac{1}{x} = 0\)

\(=> x + \frac{1}{x} = -4\)

So, \((x + \frac{1}{x})^2 = (-4)^2\) and \(x^2 +2x(\frac{1}{x}) + \frac{1}{x^2} = 16.\)

Therefore,
\(x^2 +2 + \frac{1}{x^2} = 16\)

and \(x^2 + \frac{1}{x^2} = 14.\)

Therefore, the answer is C.
Answer: C
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Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?   [#permalink] 03 May 2019, 00:16
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