If x + 1 = 3 , then the value of x5 + 1 is xx5

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Using Rule 1 and 8,

	x +	1		²	= x² +	1	+ 2
		x				x²

⇒ x² +	1	= 9 - 2 = 7
	x²

Again ,

	x +	1		³	= x³ +	1	+ 3		x +	1
		x				x³				x

⇒ 27 = x³ +	1	+ 3 × 3
	x³

⇒ x³ +	1	= 18
	x³

∴		x² +	1			x³ +	1		= 7 × 18 = 126
			x²				x³

⇒ x⁵ +		x +	1		+	1	= 126
			x			x⁵

⇒ x⁵ +	1	= 126 – 3 = 123
	x⁵