If x4 + 1 = 47, what will be the value of x3 +1

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x⁴ +	1	= 47
	x⁴

⇒ (x²)²		1		²	= 47
		x²

⇒		x² +	1		²	– 2 = 47
			x²

[∵ a² + b² = (a + b)² – 2ab]

⇒		x² +	1		²	= 47 + 2 = 49
			x²

⇒ x² +	1	= √49 = 7
	x²

Again,		x +	1		²	– 2 = 7
			x

⇒		x +	1		²	= 7 + 2 = 9
			x

⇒ x +	1	= √9 = 3
	x

On cubing both sides,

	x +	1		³	= 3³
		x

⇒ x³ +	1	+ 3		x +	1		= 27
	x³				x

⇒ x³ +	1	+ 3 × 3 = 27
	x³

⇒ x³ +	1	= 27 – 9 = 18
	x³