If ; x > 1, then what is the value of x2 - 3x + 2 equal to ?

 Shortcut Trick

Clearly we can see, at x = 6,

LHS = RHS

Therefore,

x2 - 3x + 2 = 6² - 3 × 6 + 2

x2 - 3x + 2 = 36 - 18 + 2

∴ x2 - 3x + 2 = 20

Alternate MethodGiven:

Calculate

Concept Used:

Recurrence and simplification of nested fractions followed by algebraic simplification.

Calculation:

Let's solve the recurrence:

⇒ Let .

⇒ Then

⇒ Substitute back in, where

⇒

⇒

⇒

⇒

⇒

⇒ or (Since , )

Now, calculate :

⇒ Substitute into ,

⇒

⇒

⇒

∴ .