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

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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17 Oct 2018, 02:31
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15% (low)

Question Stats:

87% (00:53) correct 13% (02:40) wrong based on 55 sessions

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If $$x + \frac{1}{x} = 5$$, what is $$x^2 + \frac{1}{x^2}$$?

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

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Math Expert
Joined: 02 Aug 2009
Posts: 7757
Re: If x + 1/x = 5, what is x^2 + 1/x^2?  [#permalink]

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17 Oct 2018, 04:34
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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17 Oct 2018, 06:29
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

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

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18 Oct 2018, 18:17
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

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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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08 Nov 2018, 06:09
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Re: if x+(1/x) = 5, what is x^2+(1/x^2)? a. 5 b. 12 c. 13   [#permalink] 08 Nov 2018, 06:09
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