If $$x + \frac{1}{x} = 2,$$   x ≠ 0, then the value of $${x^2}{\text{ + }}\frac{1}{{{x^3}}}$$   is equal to?

A. 1

B. 2

C. 3

D. 4

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {\text{ }}x + \frac{1}{x} = 2{\text{, }}\,\,\,x \ne 0 \cr & {\text{Put }}x = 1 \cr & 1 + 1 = 2 \cr & \therefore {x^2}{\text{ + }}\frac{1}{{{x^2}}} \cr & = 1 + 1 \cr & = 2 \cr} $$