If x + 1 = √3 , then the value of x30 + x24 + x18

Home » Aptitude » Algebra » Question

Using Rule 8,

x +	1	= √3
	x

On cubing both sides,

⇒ x³ +	1	+ 3		x +	1		= 3√3
	x³				x

⇒ x³ +	1	+ 3√3 = 3√3
	x³

⇒ x³ +	1	= 0
	x³

∴ Expression = x³⁰ + x²⁴ + x¹⁸ + x¹² + x⁶ + 1
Expression = x²⁴( x⁶ + 1 ) + x¹²( x⁶ + 1 ) + 1( x⁶ + 1 )
Expression = ( x⁶ + 1 )( x²⁴ + x¹² + 1 )

Expression = x³		x³ +	1		( x²⁴ + x¹² + 1 ) = 0
			x³

If x +	1	= √3 , then the value of x³⁰ + x²⁴ + x¹⁸ + x¹² + x⁶ + 1 is
	x