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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
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Updated on: 25 Sep 2016, 01:37
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:13) correct 29% (02:19) wrong based on 192 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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 24 Sep 2016, 21:46. Last edited by Bunuel on 25 Sep 2016, 01:37, edited 2 times in total. Renamed the topic and edited the question. Board of Directors Status: Stepping into my 10 years long dream Joined: 18 Jul 2015 Posts: 3631 Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 24 Sep 2016, 22:09 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 _________________ My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub | Importance of an Error Log! Verbal Resources: All SC Resources at one place | All CR Resources at one place GMAT Club Inbuilt Error Log Functionality - View More. New Visa Forum - Ask all your Visa Related Questions - here. New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Check our new About Us Page here. Math Expert Joined: 02 Sep 2009 Posts: 53066 Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 25 Sep 2016, 01:49 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 _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4391 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 25 Sep 2016, 06:59 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 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) CEO Joined: 11 Sep 2015 Posts: 3446 Location: Canada If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 25 Sep 2016, 07:27 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: RELATED VIDEO _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 27 Sep 2016, 08:07 ==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 19 Jul 2017
Posts: 85
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Concentration: General Management, Strategy
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17 Sep 2017, 06:58
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
Manager
Joined: 12 Feb 2017
Posts: 70

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26 Sep 2017, 22:08
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

Kudos if it helps.
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Joined: 19 Oct 2013
Posts: 508
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

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13 Oct 2018, 01:20
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
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If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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24 Jan 2019, 05:30
[Math Revolution GMAT math practice question]

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

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

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 09 Mar 2018 Posts: 1002 Location: India Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)? [#permalink] ### Show Tags 24 Jan 2019, 05:45 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 Answer C _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4391 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)? [#permalink] ### Show Tags 24 Jan 2019, 07:03 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x+(1/x)=4, x2+(1/x2)=? [#permalink] ### Show Tags 27 Jan 2019, 17:26 => $$( x + \frac{1}{x} )^2 = x^2 + 2x(\frac{1}{x}) + (\frac{1}{x})^2 = x^2 + (\frac{1}{x})^2 + 2 = 4^2 = 16.$$ Thus, $$x^2 + (\frac{1}{x})^2 = ( x + \frac{1}{x} )^2 - 2 = 16 - 2 = 14.$$ Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If x+(1/x)=4, x2+(1/x2)=?   [#permalink] 27 Jan 2019, 17:26
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