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If x + 1/x = 5, what is x^2 + 1/x^2?

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If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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New post 17 Oct 2018, 01:31
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E

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  15% (low)

Question Stats:

86% (00:50) correct 14% (01:54) wrong based on 49 sessions

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Re: If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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New post 17 Oct 2018, 03:34
Bunuel wrote:
If \(x + \frac{1}{x} = 5\), what is \(x^2 + \frac{1}{x^2}\)?

A. 5
B. 12
C. 13
D. 20
E. 23


\(x + \frac{1}{x} = 5\)
Square both sides... \((x + \frac{1}{x})^2 = 5^2........x^2+\frac{1}{x^2}+2=25..........x^2+\frac{1}{x^2=25-2=23}\)

E
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Re: If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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New post 17 Oct 2018, 05:29
Top Contributor
Bunuel wrote:
If \(x + \frac{1}{x} = 5\), what is \(x^2 + \frac{1}{x^2}\)?

A. 5
B. 12
C. 13
D. 20
E. 23


If we recognize that SQUARING x gives us x², and SQUARING 1/x gives us 1/x², then we might try SQUARING both sides of our given equation.

That is: (x + 1/x)² = 5²
In other words: (x + 1/x)(x + 1/x) = 25
Use FOIL to expand: x² + 1 + 1 + 1/x² = 25
Simplify: x² + 2 + 1/x² = 25
Subtract 2 from both sides to get: x² + 1/x² = 23

Answer: E

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Brent
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Re: If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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New post 18 Oct 2018, 17:17
Bunuel wrote:
If \(x + \frac{1}{x} = 5\), what is \(x^2 + \frac{1}{x^2}\)?

A. 5
B. 12
C. 13
D. 20
E. 23


If we square both sides of the equation x + 1/x = 5, we have:

x^2 + 2(x)(1/x) + 1/x^2 = 25

x^2 + 2 + 1/x^2 = 25

x^2 + 1/x^2 = 23

Answer: E
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Re: if x+(1/x) = 5, what is x^2+(1/x^2)? a. 5 b. 12 c. 13   [#permalink]

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New post 08 Nov 2018, 05:09
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Re: if x+(1/x) = 5, what is x^2+(1/x^2)? a. 5 b. 12 c. 13 &nbs [#permalink] 08 Nov 2018, 05:09
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