Question

if x=3+2root2,find x+1/x is rational or irrational

Answer 1

x=3+2root2
then, 1/x=1/3+2root2
=1/3+2root2×3-2root2/3-2root2
=3-2root2/3^2-2root2^2
=3-2root2/9-8
=3-2root2/1
x+1/× = 3+2root2+3-2root2
= 3+3 =6
so,6 is the rational number .