If x + 1 = 0 , then the value of x5 + 1 is xx5

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Using Rule 1 and 8,

x +	1	= 0
	x

On squaring both sides,

⇒		x +	1		²	= 0
			x

⇒ x² +	1	+ 2 = 0
	x²

⇒ x² +	1	= – 2 ..... (i)(not admissible)
	x²

On cubing , x +	1	= 0
	x

⇒ x³ +	1	+ 3 × 0 = 0
	x³

⇒ x³ +	1	= 0
	x³

∴		x² +	1			x³ +	1		= 2 × 2 = 4
			x²				x³

⇒ x⁵ +	1	+ x +	1	= 0
	x⁵		x

⇒ x⁵ +	1	= 0
	x⁵