If x = 3 + 2√2 , then the value of x6 + x4 + x2 +

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Expression =	x⁶ + x⁴ + x² + 1
	x³

Expression =	x⁶	+	x⁴	+	x²	+	1
	x³		x³		x³		x³

Expression = x³ + x +	1	+	1
	x		x³

Expression =		x³ +	1		+		x +	1
			x³					x

Expression =

x +

- 3

x +

Expression =		x +	1		³	- 2		x +	1		---(i)
			x						x

Now, x = 3 + 2√2

∴	1	=	1
	x		3 + 2√2

=	1	×	3 - 2√2
	3 + 2√2		3 - 2√2

	1	=	3 - 2√2
	x		9 - 8

∴ x +	1	= 3 + 2√2 + 3 - 2√2 = 6
	x

∴ Expression = (6)³ - 2 × 6 = 216 –12 = 204

If x = 3 + 2√2 , then the value of	x⁶ + x⁴ + x² + 1	is equal to
	x³