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

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Using Rule 1 and 8,

x +	1	= 3
	x

On squaring both sides,

⇒		x +	1		²	= 9
			x

⇒ x² +	1	+ 2 = 9
	x²

⇒ x² +	1	= 9 – 2 = 7 ... (i)
	x²

Again,

⇒		x +	1		³	= (3)³ = 27
			x

⇒ x³ +	1	+ 3		x +	1		= 27
	x³				x

⇒ x³ +	1	+ 3 × 3 = 27
	x³

∴ x³ +	1	= 27 - 9 = 18 ...(ii)
	x³

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

⇒ x⁵ +	1	+ x +	1	= 126
	x⁵		x

⇒ x⁵ +	1	= 126 – 3 = 123
	x⁵