Question

if x =3+2√2, check whether x+ 1÷x is rational number or irrational

Answer 1

1/x=1/3+2rt2=3-2rt

x+1/x=3+2rt2+3-2rt2=6

Therefore it is rational

Answer 2

1/x = 1/(3+2√2)
= (3-2√2)/(9-8)
= 3-2√2

so
x + 1/x
= (3+2√2) + (3-2√2)
= 6

so it's rational

hope it helps you
@di