What is the simplified value of ( x + 1/x ) ( x^2 + 1x^2 ) ( x^4 + 1x^4 ) ( x^8 + 1x^8 ) ( x^16 + 1x^16 ) is:

Option D. ( x^32 - 1x^32 ) ( x - 1/x ). Answer & Solution Answer: Option D Solution: & ( x + 1/x ) ( x^2 + 1x^2 ) ( x^4 + 1x^4 ) ( x^8 + 1x^8 ) ( x^16 + 1x^16 ) & [ ( x - 1/x ) ( x + 1/x ) ( x^2 + 1x^2 ) ( x^4 + 1x^4 ) ( x^8 + 1x^8 ) ( x^16 + 1x^16 ) ]x - 1/x & [ ( x^2 - 1x^2 ) ( x^2 + 1x^2 ) ( x^4 + 1x^4 ) ( x^8 + 1x…

What is the simplified value of ( x + 1/x ) ( x^2 + 1x^2 ) ( x^4 + 1x…

Answer: Option D

Solution:

\Rightarrow (x + \frac{1}{x}) (x^{2} + \frac{1}{x ^{2}}) (x^{4} + \frac{1}{x ^{4}}) (x^{8} + \frac{1}{x ^{8}}) (x^{16} + \frac{1}{x ^{16}}) \Rightarrow \frac{[ ( x - \frac{1}{x} ) ( x + \frac{1}{x} ) ( x ^{2} + \frac{1}{x ^{2}} ) ( x ^{4} + \frac{1}{x ^{4}} ) ( x ^{8} + \frac{1}{x ^{8}} ) ( x ^{16} + \frac{1}{x ^{16}} ) ]}{x - \frac{1}{x}} \Rightarrow \frac{[ ( x ^{2} - \frac{1}{x ^{2}} ) ( x ^{2} + \frac{1}{x ^{2}} ) ( x ^{4} + \frac{1}{x ^{4}} ) ( x ^{8} + \frac{1}{x ^{8}} ) ( x ^{16} + \frac{1}{x ^{16}} ) ]}{x - \frac{1}{x}} \Rightarrow \frac{[ ( x ^{4} - \frac{1}{x ^{4}} ) ( x ^{4} + \frac{1}{x ^{4}} ) ( x ^{8} + \frac{1}{x ^{8}} ) ( x ^{16} + \frac{1}{x ^{16}} ) ]}{x - \frac{1}{x}} \Rightarrow \frac{[ ( x ^{8} - \frac{1}{x ^{8}} ) ( x ^{8} + \frac{1}{x ^{8}} ) ( x ^{16} + \frac{1}{x ^{16}} ) ]}{x - \frac{1}{x}} \Rightarrow \frac{[ ( x ^{16} - \frac{1}{x ^{16}} ) ( x ^{16} + \frac{1}{x ^{16}} ) ]}{x - \frac{1}{x}} \Rightarrow \frac{x ^{32} - \frac{1}{x ^{32}}}{x - \frac{1}{x}}