Question

if x= 4-√5 find the value of x+1/x​

Answer 1

Step-by-step explanation:

just rationalize 1/x and add it.

Answer 2

$x = 4 - \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{4 - \sqrt{5} } \\ \frac{1}{x} = \frac{1}{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ \frac{1}{x} = \frac{4 + \sqrt{5} }{16 - 5} \\ \frac{1}{x} = \frac{4 + \sqrt{5} }{11} \\ \\ x + \frac{1}{x} = 4 - \sqrt{5} + \frac{4 + \sqrt{5} }{11} \\ x + \frac{1}{x} = \frac{44 - 11 \sqrt{5} + 4 + \sqrt{5} }{11} \\ = \frac{48 - 10 \sqrt{5} }{11}$