If x2 − 3x + 1 = 0, then the value of

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x² − 3x + 1 = 0
⇒ x² + 1 = 3x
Dividing both sides by x,

⇒ x +	1	= 3
	x

∴ x² + x +	1	+	1
	x		x²

=		x² +	1		+		x +	1
			x²					x

=		x +	1		²	− 2 +		x +	1
			x						x

= 9 – 2 + 3 = 10