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

Question

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 https://www.GMATinsight.com

GMATinsight · Answer

(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

umasarath52 · Answer

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

Answer D

ENGRTOMBA2018 · Answer

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. graph.png

mvictor · Answer

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.

ruchikasingh8 · Answer

This question gets simple only if you remember that if power of any value is 0 it will be equal to 1 OR if value is 1 then no matter the power it will be 1
So here do this (x^2 - x -1)^(x+2) = 1
either x+2=0 OR (x^2 - x -1)= 1
solving both we get x = -2 OR x= 2,1 
also notice you can substitute x with 0 and get 1 as final answer 
i.e. (x^2 - x -1)^(x+2) => (0-0-1)^(0+2) => (-1)^2 => 1
hence different values that x can take is, -2,0,1,2

And so the answer is (D)

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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