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If x^2=2x+1, x^3=?

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Math Revolution GMAT Instructor
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If x^2=2x+1, x^3=?  [#permalink]

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New post 01 Mar 2017, 03:54
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A
B
C
D
E

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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Re: If x^2=2x+1, x^3=?  [#permalink]

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New post 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
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Math Revolution GMAT Instructor
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Re: If x^2=2x+1, x^3=?  [#permalink]

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New post 03 Mar 2017, 00:13
==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)

Answer: B
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Re: If x^2=2x+1, x^3=?  [#permalink]

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New post 06 Mar 2017, 17:38
1
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

Answer: B
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Re: If x^2=2x+1, x^3=?  [#permalink]

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New post 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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Re: If x^2=2x+1, x^3=?  [#permalink]

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Re: If x^2=2x+1, x^3=?   [#permalink] 14 Mar 2020, 23:48

If x^2=2x+1, x^3=?

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