If x + 1 = √3 ,then the value of x18 + x12 + x6 +

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Using Rule 8,

x +	1	= √3
	x

Cubing both sides,

∴ x³ +	1	+ 3		x +	1		= ( √3 )³
	x³				x

⇒ x³ +	1	+ 3√3 = 3√3
	x³

⇒ x³ +	1	= 0
	x³

Now , x¹⁸ + x¹² + x⁶ + 1 = x¹²( x⁶ + 1 ) + 1( x⁶ + 1 )
= ( x¹² + 1 )( x⁶ + 1 )

= ( x¹² + 1 ).x³		x³ +	1		= 0
			x³

If x +	1	= √3 ,then the value of	x¹⁸ + x¹² + x⁶ + 1	is
	x