Question

if x=3+ 2 √2 then x+1/x=?

Answer 1

x = 3+2√2

1/x = 1/(3+2√2)

by rationalizing the denominator ,

1/x = (3-2√2)/(3+2√2)(3-2√2)
1/x = (3-2√2)/(3²-(2√2)²)

${x}^{2} - {y}^{2} = (x + y)(x - y)$
1/x = (3-2√2)/(9-8)
1/x = (3-2√2)/1 => 3-2√2


x + 1/x = 3+2√2+3-2√2

x + 1/x = 3+3 = 6


hope this helps