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x² – 4x + 1 = 0
⇒ x² + 1 = 4x

⇒	x² + 1	=	4x
	x		x

⇒ x +	1	= 4
	x

On cubing both sides,

	x +	1		³	= 64
		x

x³ +	1	+ 3		x +	1		³	= 64
	x³				x

⇒ x³ +	1	+ 3 × 4 = 64
	x³

⇒ x³ +	1	= 64 - 12 = 52
	x³

⇒	x⁶ + 1	= 52
	x³