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If x^2 +
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16 Feb 2021, 05:36
16 Feb 2021, 05:36
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Question Stats:
56% (01:02) correct
43% (02:05) wrong based on 57 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. 10
B. 12
C. 14
D. 16
E. 18
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 10
B. 12
C. 14
D. 16
E. 18
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
If x^2 +
[#permalink]
16 Feb 2021, 05:50
16 Feb 2021, 05:50
2
Hi,
Although this question might look difficult but it is not. It can be solved in under 1 min without writing.
x^2+1/x^2=4
Squaring both side
x^4+ 2 * x^2 * 1/x^2 + x^4= 16
we can cancel x^2
x^4+2+1/x^4= 16
x^4+1/x^4=16-2
x^4+x^1/x^4=14.
IMO C
Hope this helps
Although this question might look difficult but it is not. It can be solved in under 1 min without writing.
x^2+1/x^2=4
Squaring both side
x^4+ 2 * x^2 * 1/x^2 + x^4= 16
we can cancel x^2
x^4+2+1/x^4= 16
x^4+1/x^4=16-2
x^4+x^1/x^4=14.
IMO C
Hope this helps
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x^2 +
[#permalink]
16 Feb 2021, 06:51
16 Feb 2021, 06:51
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1
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Carcass wrote:
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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 10
B. 12
C. 14
D. 16
E. 18
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
Cheers,
Brent
