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If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?

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Math Revolution GMAT Instructor
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If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?  [#permalink]

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Updated on: 18 Jan 2016, 22:21
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25% (medium)

Question Stats:

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If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?

A. 21
B. 22
C. 23
D. 24
E. 27

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Originally posted by MathRevolution on 14 Jan 2016, 18:02.
Last edited by Bunuel on 18 Jan 2016, 22:21, edited 1 time in total.
Edited the question.
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Re: If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?  [#permalink]

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15 Jan 2016, 07:15
Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2

x^2 + (1/x)^2 = 23

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6806
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?  [#permalink]

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18 Jan 2016, 18:17
If x+(1/x)=5, what is the value of x^2+(1/x)^2?

A. 21
B. 22
C. 23
D. 24
E. 27

==>x^2+(1/x)^2=(x+1/x)^2-2x(1/x)=25-2=23. Therefore, the answer is C.
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Re: If x + (1/x) = 5, what is the value of x^2 + (1/x)^2?  [#permalink]

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03 Jan 2018, 01:48
x + (1/x) = 5
(x+(1/x))^2 = 5^2
x^2 + 2 + (1/x)^2 = 25
x^2 + (1/x)^2 = 23

Option C
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Re: If x + (1/x) = 5, what is the value of x^2 + (1/x)^2? &nbs [#permalink] 03 Jan 2018, 01:48
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