If average of two numbers x and 1 (where x ≠ 0) is A,

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If average of two numbers x and 1 (where x ≠ 0) is A, what will be the average of x³ 1 ?
x x³

According to the question ,

⇒ x +	1	= 2A
	x

On cubing both sides,

⇒		x +	1		³	= (2A)³ = 8A³
			x

⇒ x³ +	1	+ 3		x +	1		= 8A³
	x³				x

⇒ x³ +	1	+ 3 × 2A = 8A³
	x³

⇒ x³ +	1	= 8A³ - 4A
	x³

Required average =	8A³ - 4A	= 4A³ - 2A
	2

If average of two numbers x and	1	(where x ≠ 0) is A, what will be the average of x³	1	?
	x		x³