Question

Prove that 1/(3 - 2sqrt(5)) is an irrational number.​

Answer 1

Answer:

Assume that 3+2

5

is rational. Then,

3+2

5

=

b

a

5

=

2b

a−3b

This gives that

2b

a−3b

is rational but

5

is an irrational number, therefore, the assumption is wrong.

Hence, 3+2

5

is irrational