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Re: If x^2 = x + 1, which of the following is equal to x^3 ? [#permalink]
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Jake7Wimmer wrote:
Can someone show how to do this with plugging in numbers please.

Solutions of ­x^2 = x + 1 are \(x = \frac{1-\sqrt{5}}{2}\) and \(x = \frac{1 + \sqrt{5}}{2}\)­. Thus, plugging values it not a good idea for this question. ­
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Re: If x^2 = x + 1, which of the following is equal to x^3 ? [#permalink]
Jake7Wimmer wrote:
Can someone show how to do this with plugging in numbers please.


The characteristics equation of x^2=x+1 follow the reoccurrence a_n=a_{n-1}+a_{n-2}. , commonly referred to as Fibonacci sequence.

This equation gives golden ratio and inverse of golden ratio as its roots

x^3 is equivalent to a_3 .
x^2 is a_2
x is a_1
1 is 1



You can find a_3 in terms of a_1
a_3=a_2+a_1=a_1+1+a_1=2a_1+1

This corresponds to 2x+1

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Re: If x^2 = x + 1, which of the following is equal to x^3 ? [#permalink]
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