If x2 – 3x + 1 = 0, then the value of x6 + x4 + x2 + 1

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x² – 3 x + 1 = 0
⇒ x² + 1 = 3 x

⇒	x² + 1	= 3
	x

⇒ x +	1	= 3 ........... (i)
	x

∴ Expression =	x⁶ + x⁴ + x² + 1
	x³

Expression =	x⁶	+	x⁴	+	x²	+	1
	x³		x³		x³		x³

Expression = x³ + x +	1	+	1
	x		x³

Expression =		x³ +	1		+		x +	1		= 2 × 2 = 4
			x³					x

Expression =

x +

- 3 . x .

x +

Expression = 3³ – 3 × 3 + 3 = 27 – 9 + 3 = 21

If x² – 3x + 1 = 0, then the value of	x⁶ + x⁴ + x² + 1	will be
	x³