Question

a) If x2 - 4x + 1 = 0, find x3 -
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Answer 1

x² - 4x +1 = 0

x * x - 4x +1 = 0

x * x = -1 + 4x

x = -1 + 4x/x

x = -1 + 4x

x³ = -1 + 4x * (-1 + 4x) *(-1+4x)

x³ = +1 -4x -4x +16x² * ( -1+4x)

x³ = +1 -8x +16x² * (-1+4x)

x³ = -1 +4x +8x - 32x² -16x² + 64x²

x³ = -1 + 12x -48x² +64x²

x³ = -1 +12x +16x²