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CEO  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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1
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Difficulty:   95% (hard)

Question Stats: 28% (01:43) correct 72% (01:37) wrong based on 69 sessions

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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.
CEO  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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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

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GMATinsight
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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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By substituting the values, -2,-1,0,2

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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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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

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 [ 10.34 KiB | Viewed 1249 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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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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# Suppose x is an integer such that [m](x^2 - x - 1)^ {(x+2)} =1[/m]  