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# x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8014
GMAT 1: 760 Q51 V42
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x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?  [#permalink]

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01 May 2019, 00:49
4
7
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:00) correct 44% (02:48) wrong based on 43 sessions

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[GMAT math practice question]

$$x^2 + 4x + 1 = 0$$. 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2978 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2? [#permalink] ### Show Tags 01 May 2019, 01:07 2 1 MathRevolution wrote: [GMAT math practice question] $$x^2 + 4x + 1 = 0$$. What is the value of $$x^2 + \frac{1}{x^2}$$? $$A. 10$$ $$B. 12$$ $$C. 14$$ $$D. 16$$ $$E. 18$$ i.e. $$x^2 + 4x + 1 = 0$$ Dividing both sides by x we get i.e. $$x + 4 + \frac{1}{x} = 0$$ i.e. $$x + \frac{1}{x} = -4$$ Squaring both sides we get $$x^2 + \frac{1}{x^2}+2*x*\frac{1}{x} = 16$$ i.e. $$x^2 + \frac{1}{x^2} = 14$$ Answer: Option C _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION ##### General Discussion Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8014 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2? [#permalink] ### Show Tags 03 May 2019, 00:16 => $$x^2 + 4x + 1 = 0$$ $$=> x + 4 + \frac{1}{x} = 0$$ $$=> x + \frac{1}{x} = -4$$ So, $$(x + \frac{1}{x})^2 = (-4)^2$$ and $$x^2 +2x(\frac{1}{x}) + \frac{1}{x^2} = 16.$$ Therefore, $$x^2 +2 + \frac{1}{x^2} = 16$$ and $$x^2 + \frac{1}{x^2} = 14.$$ 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$79 for 1 month Online Course"
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Re: x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2?   [#permalink] 03 May 2019, 00:16
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