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# How many integers x satisfy the equation (x^2 − x − 1)^(x + 2) = 1 ?

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Re: How many integers x satisfy the equation (x^2 − x − 1)^(x + 2) = 1 ? [#permalink]
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Case 1: Exponent is zero -> x = -2

Case 2: Base is equal to 1; In that case x^2 – x – 1 = 1 => x = 2 or x = -1

Case 3: Base is equal to -1 and exponent is even; In that case x^2 – x = 0; x = 0 or x = 1; However, for x =1, the base will be -1 and exponent will be 3. So, x = 0 is the only option in this case

So, the equation is true for x = -2, -1, 0 and 2; The answer is C

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Re: How many integers x satisfy the equation (x^2 x 1)^(x + 2) = 1 ? [#permalink]
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Re: How many integers x satisfy the equation (x^2 x 1)^(x + 2) = 1 ? [#permalink]
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