Question

If x=3 +2√2, check whether x+1/x is rational or irrational ​

Answer 1

Answer:

For simplification when finding the value of 1/x rationalize by 3-2 ½ this as numerator

x=3 + 2(2) ½

(1/x) =1/[3+2(2)½]

Now rationalize

(1/x) = 1/[3+2(2)½]

( [3-2(2)½] / [3-2(2)½] )

(1/x) = [3-2(2)½] / [3²-2 (2½)²]

(1/x) = [3-2(2)½] / [9-8] =3-2(2)½

x + (1/x) = 3+2(2)½ + 3 - 2(2)½=6

As 6 is rational hence x+1/x is rational