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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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If x+(1/x)=4, x2+(1/x2)=?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 70% (01:10) correct 30% (02:14) wrong based on 212 sessions

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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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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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MathRevolution wrote:
If x+(1/x)=4, $$x^2+(1/x^2)$$=?

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

Similar question: if-x-2-1-x-2-4-what-is-the-value-of-x-4-1-x-175113.html
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Re: If x+(1/x)=4, x2+(1/x2)=?  [#permalink]

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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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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

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

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==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
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Re: If x+(1/x)=4, x2+(1/x2)=?  [#permalink]

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

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X + 1/x = 4

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

x^2 + 2 (x * 1/x) + 1/x^2 = 16

x^2 + 2 + 1/x^2 = 16

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

ArjunJag1328 check the above it may clarify your question.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})?$$

$$A. 10$$
$$B. 12$$
$$C. 14$$
$$D. 16$$
$$E. 18$$
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Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})?$$

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

Manipulate the if part as

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

x^2 + 1/x^2 = 16 - 2

= 14

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Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})?$$

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

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

Squaring both sides we have -

$$x^2 + 2*x*\frac{1}{x} + \frac{1}{x^2} = 16$$

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

Or, $$x^2 +\frac{1}{x^2} = 14$$, Thus Answer must be (C)

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Thanks and Regards

Abhishek....

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x+(1/x)=4, x2+(1/x2)=?  [#permalink]

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=>

$$( x + \frac{1}{x} )^2 = x^2 + 2x(\frac{1}{x}) + (\frac{1}{x})^2 = x^2 + (\frac{1}{x})^2 + 2 = 4^2 = 16.$$
Thus, $$x^2 + (\frac{1}{x})^2 = ( x + \frac{1}{x} )^2 - 2 = 16 - 2 = 14.$$

Therefore, the answer is C.
_________________ Re: If x+(1/x)=4, x2+(1/x2)=?   [#permalink] 27 Jan 2019, 18:26
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