If t2 – 4t + 1 = 0, then the value of t3 + 1 is t3

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t² – 4t + 1 = 0
⇒ t² + 1 = 4t

⇒	t² + 1	= 4
	t

⇒ t +	1	= 4
	t

On cubing both sides,

⇒		t +	1		³	= 4³
			t

⇒ t³ +	1	+ 3		t +	1		= 64
	t³				t

⇒ t³ +	1	+ 3 × 4 = 64
	t³

⇒ t³ +	1	= 64 – 12 = 52
	t³