If x4 + 1 = 119 , then the values of x3 + 1 are x4x3

Home » Aptitude » Algebra » Question

x⁴ +	1	= 119
	x⁴

⇒		x² +	1		²	- 2 = 119
			x²

⇒		x² +	1		²	= 119 + 2 = 121
			x²

⇒		x² +	1		²	= (11)²
			x²

⇒ x² +	1	= 11
	x²

Again,		x +	1		²	- 2 = 11
			x

⇒		x +	1		²	= 11 + 2 = 13
			x

⇒ x +	1	= ± √13
	x

On cubing both sides,

⇒		x +	1		³	= ( ± √13 )³
			x

⇒ x³ +	1	+ 3 . x .	1		x +	1		= ± √13
	x³		x			x

⇒ x³ +	1	+ 3 × ( ± √13 ) = ± √13
	x³

⇒ x³ -	1	= ± (13√13 - 3√13) = ± 10√13
	x³