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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?

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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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New post 26 Jul 2014, 09:59
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If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 10
B. 12
C. 14
D. 16
E. 18
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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New post 26 Jul 2014, 10:09
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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New post 17 Mar 2016, 21:44
1
Squaring on both sides:\((x^2 + \frac{1}{x^2})^2 = 16\)
\(x^4 + \frac{1}{x^4} + 2 = 16\)
\(x^4 + \frac{1}{x^4} = 14\)

Answer: D
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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New post 21 Mar 2016, 04:26
If x^2+(1/x^2)=4, x^4+(1/x^4)=?

A. 10
B. 11
C. 12
D. 14
E. 15


-> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=4^2-2=14.
Thus, the answer is D.
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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New post 20 Apr 2016, 07:19
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1
Reni wrote:
If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?

A. 10
B. 12
C. 14
D. 16
E. 18


IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 4 and SQUARE both sides:

(x² + 1/x²)² = 4²
So, (x² + 1/x²)(x² + 1/x²) = 16
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 16
Simplify: x⁴ + 1/x⁴ = 14

Answer: C

Related Resource: Here's a free video on using the FOIL method to expand expressions: https://www.gmatprepnow.com/module/gmat ... /video/952

Cheers,
Brent
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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?  [#permalink]

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Re: If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ?   [#permalink] 13 Sep 2019, 01:50
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