If x = 3 + √8, then x2 + 1 is

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x = 3 + √8

∴	1	=	1	=	3 − √8
	x		3 + √8		(3 + √8)(3 − √8)

=	3 − √8	= 3 − √8
	9 − 8

Now, x² +	1	=		x +	1		²	− 2
	x²				x

= (3 + √8 + 3 − √8)² – 2
= 36 – 2 = 34