If a2 – 4a – 1 = 0, a ≠ 0, then the value of a2

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a² – 4a – 1 = 0
⇒ a² – 1 = 4a
On dividing both sides by a,

⇒ a −	1	= 4 ...(i)
	a

Expression = a² + 3a +	1	−	3
	a²		a

= a² +	1	+ 3a −	3
	a²		a

=		a −	1		²	+ 2 + 3		a −	1
			a						a

= (4)² + 2 + 3 × 4
= 16 + 2 + 12 = 30