If x + 12 = 3 , then the value of ( x72 + x66 + x54 + x36

Home » Aptitude » Algebra » Question

If x + 1 ² = 3 , then the value of ( x⁷² + x⁶⁶ + x⁵⁴ + x³⁶ + x²⁴ + x⁶ + 1 ) is
x

Using Rule 8,

		x +	1		²	= 3
			x

⇒ x +	1	= √3
	x

On cubing both sides,

⇒		x +	1		³	= 3√3
			x

∴ x³ +	1	+ 3		x +	1		= 3√3
	x³				x

⇒ x³ +	1	+ 3√3 = 3√3
	x³

⇒ x³ +	1	= 0 ⇒ x⁶ + 1 = 0
	x³

Now , x⁷² + x⁶⁶ + x⁵⁴ + x³⁶ + x²⁴ + x⁶ + 1 = ( x⁶ )¹² + ( x⁶ )¹¹ + ( x⁶ )⁹ + ( x⁶ )⁶ + ( x⁶ )⁴ + ( x⁶ ) + 1
= 1 – 1 – 1 + 1 + 1 + 0 = 1

If		x +	1		²	= 3 , then the value of ( x⁷² + x⁶⁶ + x⁵⁴ + x³⁶ + x²⁴ + x⁶ + 1 ) is
			x