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# If x^2=2x+1, x^3=？

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
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01 Mar 2017, 03:54
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Difficulty:

65% (hard)

Question Stats:

59% (02:04) correct 41% (02:35) wrong based on 133 sessions

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If $$x^2=2x+1, x^3$$=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

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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 Community Reply Senior Manager Joined: 19 Apr 2016 Posts: 261 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: If x^2=2x+1, x^3=？ [#permalink] ### Show Tags 01 Mar 2017, 04:16 8 MathRevolution wrote: If $$x^2=2x+1, x^3$$=？ A. 4x B. 5x+2 C. 5x-1 D. 3x+2 E. 3x-2 $$x^2 = 2x+1$$ $$x^3 = (2x+1)*x$$ $$x^3 = 2*x^2 + x$$ $$x^3 = 2*(2x+1) + x$$ $$x^3 = 5x+1$$ Hence option B is correct Hit Kudos if you liked it ##### General Discussion Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9006 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x^2=2x+1, x^3=？ [#permalink] ### Show Tags 03 Mar 2017, 00:13 ==> $$x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2$$ Answer: B _________________ 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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06 Mar 2017, 17:38
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1
MathRevolution wrote:
If $$x^2=2x+1, x^3$$=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

Since we are given x^2 = 2x + 1 and need to determine the value of x^3, we can multiply both sides of our equation by x and we have:

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

x^3 = 2x^2 + x

We can substitute (2x + 1) for x^2 on the right hand side of the equation and obtain:

x^3 = 2(2x + 1) + x

x^3 = 4x + 2 + x

x^3 = 5x + 2

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18 Feb 2019, 00:30
MathRevolution wrote:
If $$x^2=2x+1, x^3$$=？

A. 4x
B. 5x+2
C. 5x-1
D. 3x+2
E. 3x-2

Lazy is the keyword

Multiply if statement by x

x^2 = 2x + 1

$$x^3 = 2x^2 + 1$$

Substitute for x^2 again
2(2x+1) + x
4x + 2 +x
we get 5x +2
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14 Mar 2020, 23:48
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Re: If x^2=2x+1, x^3=？   [#permalink] 14 Mar 2020, 23:48