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If x+(1/x)=4, x2+(1/x2)=?

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Math Revolution GMAT Instructor
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If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post Updated on: 25 Sep 2016, 02:37
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If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18

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Originally posted by MathRevolution on 24 Sep 2016, 22:46.
Last edited by Bunuel on 25 Sep 2016, 02:37, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 24 Sep 2016, 23:09
1
MathRevolution wrote:
(ex 12) (equation) If x+(1/x)=4, \(x^2+(1/x^2)\)=?
A. 10 B. 12 C. 14 D. 16 E. 18


x + 1/x = 4

Squaring both sides,

\((x + 1/x )^2 = 4^2\)

or \(x^2+(1/x^2) + 2 = 16\)

or \(x^2+(1/x^2) = 14\)

Hence, C
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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 25 Sep 2016, 02:49
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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 25 Sep 2016, 07:59
MathRevolution wrote:
If \(x+\frac{1}{x}\) =4, \(x^2+\frac{1}{x^2}\)= ?

A. 10
B. 12
C. 14
D. 16
E. 18


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

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

Or, \(x^2\) + \(2*x*\frac{1}{x}\)+ \(\frac{1}{x^2}\) = \(16\)

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

Or, \(x^2+\frac{1}{x^2}\) = \(16 - 2\)

Or, \(x^2+\frac{1}{x^2}\) = \(14\)

So, Answer will be C. 14

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If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 25 Sep 2016, 08:27
Top Contributor
MathRevolution wrote:
If x + (1/x) = 4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18


Given: x + (1/x) = 4

NOTE: since there are squared terms in the expression we're trying to evaluate, we should consider squaring both sides.

Square both sides: [x + (1/x)]² = 4²
Rewrite as: [x + (1/x)][x + (1/x)] = 16
Use FOIL method to expand: x² + 1 + 1 + 1/x² = 16
Simplify: x² + 2 + 1/x² = 16
Subtract 2 from both sides: x² + 1/x² = 14

Answer:

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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 27 Sep 2016, 09:07
==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
Answer: C
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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 17 Sep 2017, 07:58
MathRevolution wrote:
If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18


(x+1/x)^2 = X^2+2+1/x^2;

So x^2+1/x^2 = 16- 2 = 14;

Ans:C
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Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink]

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New post 26 Sep 2017, 23:08
x + 1/x = 4

Squaring both sides,

(x+1/x)^2 = 4^2

x^2+(1/x^2)+2*x*1/x=16
x^2+(1/x^2)+2=16
x^2+(1/x^2)=14
Hence Answer is option C.

Kudos if it helps.
Re: If x+(1/x)=4, x2+(1/x2)=?   [#permalink] 26 Sep 2017, 23:08
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