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If x^2=x+1, then x^4=?

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Math Revolution GMAT Instructor
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If x^2=x+1, then x^4=?  [#permalink]

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New post 30 Nov 2018, 02:19
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  25% (medium)

Question Stats:

69% (01:19) correct 31% (02:15) wrong based on 63 sessions

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[Math Revolution GMAT math practice question]

If \(x^2=x+1,\) then\(x^4\)=?

\(A. 3x+2\)
\(B. 3x-2\)
\(C. 2x+3\)
\(D. 2x-3\)
\(E. 3x+4\)

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Re: If x^2=x+1, then x^4=?  [#permalink]

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New post 30 Nov 2018, 04:46
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x^2=x+1,\) then\(x^4\)=?

\(A. 3x+2\)
\(B. 3x-2\)
\(C. 2x+3\)
\(D. 2x-3\)
\(E. 3x+4\)


x^2 = x + 1 => x4 = (x+1)^2 = x^2 + 1 + 2x = x + 1 + 2x + 1 = 3x + 2
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Re: If x^2=x+1, then x^4=?  [#permalink]

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New post 30 Nov 2018, 05:20
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Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x^2=x+1, then x^4=?  [#permalink]

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New post 02 Dec 2018, 19:02
=>
\(x^4 = (x^2^)2 = (x+1)^2 = x^2 + 2x + 1 = (x + 1) + 2x + 1 = 3x + 2.\)
Therefore, the answer is A.
Answer: A
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Re: If x^2=x+1, then x^4=?   [#permalink] 02 Dec 2018, 19:02
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