Question

(x+1/x)4=16 find the value of x100+1/x100​

Answer 1

Answer:

2

Step-by-step explanation:

$({x + \frac{1}{x} })^{4} = 16 \\ = > ( {x + \frac{1}{x} })^{4} = {2}^{4} \\ = > x + \frac{1}{x} = 2 \\ = > {x}^{2} + 1 = 2x \\ = > {x}^{2} - 2x + 1 = 0 \\ = > {(x - 1})^{2} = 0 \\ = > x - 1 = 0 \\ = > x = 1 \\ now \\ {x}^{100} + \frac{1}{ {x}^{100} } \\ = {1}^{100} + \frac{1}{ {1}^{100} } \\ = 1 + 1 \\ = 2$