If x + (1/x) = 2, then what is the value of x^64 + x^121 = ?

A. -2

B. 1

C. 2

D. 0

Solution:

Given, x + 1/x = 2

or, (x² + 1)/x = 2

or, x² + 1 = 2x

or, x² – 2x + 1 = 0

from algebraic formula, (a – b)² = a² – 2ab + b²

so, x² – 2x + 1 = x² – 2(1)x + 1² = (x – 1)² = 0

then, x – 1 = 0 => x = 1 …..(1)

now value of x⁶⁴ + x¹²¹

putting value of x = 1 from equation (1),

= (1)⁶⁴ + (1)¹²¹

= 1 + 1

= 2

Hence, value of x⁶⁴ + x¹²¹ = 2.

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