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Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]

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Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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New post Updated on: 09 Oct 2015, 23:36
1
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Question Stats:

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Suppose x is an integer such that \((x^2 - x - 1)^ {(x+2)} =1\) . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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Originally posted by GMATinsight on 09 Oct 2015, 22:14.
Last edited by GMATinsight on 09 Oct 2015, 23:36, edited 1 time in total.
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Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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New post 09 Oct 2015, 22:15
GMATinsight wrote:
Suppose x is an integer such that \((x^2 - x - 1)^ {(x+2)} =1\) . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

http://www.GMATinsight.com


\((x^2 -x-1)^ {(x+2)} =1\) is possible only when

Either (x ^ 2 -x-1)=1 i.e. x = 2 or -1

OR (x+2) =0 i.e. x = -2

OR x=0

i.e. Possible values of x = 0, 2, -1 and -2

Answer: option D

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Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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New post 10 Oct 2015, 02:50
By substituting the values, -2,-1,0,2

Answer D
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Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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New post 10 Oct 2015, 05:29
GMATinsight wrote:
GMATinsight wrote:
Suppose x is an integer such that \((x^2 - x - 1)^ {(x+2)} =1\) . How many possible values of x exist?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

http://www.GMATinsight.com


\((x^2 -x-1)^ {(x+2)} =1\) is possible only when

Either (x ^ 2 -x-1)=1 i.e. x = 2 or -1

OR (x+2) =0 i.e. x = -2

OR x=0

i.e. Possible values of x = 0, 2, -1 and -2

Answer: option D


There is another case of when base = exponent = 1 at the same time as \(1^{any integer} = 1\)

Based on the graph attached, the 2 curves show 3 points of intersections. 0 is not a point of intersection.

Attachment:
graph.png
graph.png [ 10.34 KiB | Viewed 1201 times ]
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Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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New post 05 Dec 2015, 12:51
I highly doubt you will see such a question on the real GMAT.
but just my 2 cents
the whole expression is equal to 1 only in case it is equal to 1, or equal to -1, but then x must be even.

first case:
(x^2-x-1)=1
x(x-1)=2
x can be 2
x can be -2
x can be -1


second case:
(x^2-x-1) = -1.
x(x-1)=0
x-1=0
x=0
x-1=0 => x=1. can't be, since (x^2-x-1)^(x+2) will not yield a positive answer.
x=0 - satisfies the condition.

again, I don't think gmat will give such a question.
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Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  [#permalink]

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Re: Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]   [#permalink] 12 Nov 2019, 20:49
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