Max@Math Revolution wrote:If x^2=x+1, then x^3=?
A. 3x+2
B. 3x-2
C. 2x+1
D. 2x-3
E. 3x+4
Alternate approach:
x²=x+1 implies that the square of x is equal only to one more than x.
Thus, the roots of this equation must be very small.
If we test x=-1, x=-1/2, x=0, x=1/2 and x=1 in the given equation, the two sides are closest in value when x=-1/2.
Thus, one of the roots must be close to -1/2.
If x=-1/2, then x³ = -1/8.
Implication:
The correct answer choice must yield a value close to -1/8 when x=-1/2.
The value yielded by
C is closest to -1/8:
2x+1 = (2)(-1/2) + 1 = 0.
The correct answer is
C.
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