### Question

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

^{64}+ x

^{121}= ?

A. -2

B. 1

C. 2

D. 0

#### Answer: C. 2

**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 x^{64} + x^{121}

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

= (1)^{64} + (1)^{121}

= 1 + 1

**= 2**

Hence, value of **x ^{64} + x^{121} = 2.**

**Read More:**

**Can you solve this number puzzle 9 + 8 = 117, 16 + 13 = 329, 19 + 11 = 830, 23 + 18 = ??**