Question

If x=2+√2, Check whether x+ 1/x is rational or irrational

Answer 1

Answer:

Step-by-step explanation:

Given x = 3+2√2

x +1/x

= 3+2√2 + 1 / 3+2√2

= 3+2√2 + 3-2√2 / 3+2√2(3-2√2)

= 3+2√2 + 3-2√2 / 3² - (2√2)²

= 3+2√2 + 3-2√2/9-8

= 3+2√2 + 3-2√2

= 6 Which can be written in p/q forrm. (6/1)

Therefore it's a rational number!.