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555-605 (Medium)|   Algebra|      
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Reni
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 26 Jul 2014, 09:59
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35% (medium)

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55% (01:21) correct 45% (01:35) wrong based on 1285 sessions

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If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 2
B. 4
C. 6
D. 14
E. 16­

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Bunuel
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 26 Jul 2014, 10:09
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Reni
If x^2 + 1/x^2 =4, what is the value of x^4 + 1/x^4 ?

A. 2
B. 4
C. 6
D. 14
E. 16­
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Squaring \(x^2 + \frac{1}{x^2} =4\) gives:

    \(x^4+2*x^2*\frac{1}{x^2}+\frac{1}{x^4}=16\);

    \(x^4+2+\frac{1}{x^4}=16\);

    \(x^4+\frac{1}{x^4}=14\)
.

Answer: D.­
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 24 Feb 2024, 11:18
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Reni
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 2
B. 4
C. 6
D. 14
E. 16­

Show Spoiler
Attachment:
Screenshot 2024-02-24 at 16.19.52.png
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­
Similar questions to practice (in increasing order of difficulty):

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 ­­
Hope it helps.­
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 29 Oct 2023, 11:52
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yrozenblum
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\)?

A. 2
B. 4
C. 6
D. 14
E. 16
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Remember you can solve the question just by squaring both side and subtract -2

Will correspond to 14

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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 29 Oct 2023, 11:57
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yrozenblum
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\)?

A. 2
B. 4
C. 6
D. 14
E. 16
Show more

\(x^2 + \frac{1}{x^2} = 4\)

Squaring both sides we get

\((x^2)^2 + (\frac{1}{x^2})^2 + 2*x^2*\frac{1}{x^2} = (4)^2\)

\(x^4 + \frac{1}{x^4} + 2 = 16\)

\(x^4 + \frac{1}{x^4} = 16 - 2 = 14\)

Option D
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 19 Jun 2024, 12:13
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­Classic (x + y)^2 recognition:

­
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 27 Jun 2025, 19:49
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Bunuel

Reni
If \(x^2 + \frac{1}{x^2} = 4\), what is the value of \(x^4 + \frac{1}{x^4}\) ?

A. 2
B. 4
C. 6
D. 14
E. 16­

Show Spoiler
Attachment:
Screenshot 2024-02-24 at 16.19.52.png
­
Similar questions to practice (in increasing order of difficulty):

  1. https://gmatclub.com/forum/if-x-1-x-5-w ... 79230.html
  2. https://gmatclub.com/forum/if-x-1-x-2-w ... 39575.html
  3. https://gmatclub.com/forum/if-x-2-1-x-2 ... 46397.html
  4. https://gmatclub.com/forum/if-x-1-x-4-w ... 26125.html
  5. https://gmatclub.com/forum/what-is-the- ... 09905.html
  6. https://gmatclub.com/forum/if-x-1-x-40- ... 75256.html
  7. https://gmatclub.com/forum/given-x-1-x- ... 74879.html
  8. https://gmatclub.com/forum/if-x-1-x-1-5 ... 36997.html
  9. https://gmatclub.com/forum/if-x-4-1-x-4 ... 46658.html
  10. https://gmatclub.com/forum/if-x-1-x-3-t ... 17507.html
  11. https://gmatclub.com/forum/if-x-2-4x-1- ... 94797.html
  12. https://gmatclub.com/forum/if-x-8-1-x-8 ... 39576.html
­
Hope it helps.­
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If x^2 + 1/x^2 = 4, what is the value of x^4 + 1/x^4 ? 08 Jul 2026, 06:35
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