Question

prove that 5-2√5 is irrational​

Answer 1

Answer:

Let us assume on the contrary that 5+​​ root 2 is rational.

Then, there exist co-prime a and b(b not equal to 0), such that

5+ root 2= a by b

= root 2= a by b--2

= root 2 =a--2b by b

= root 2 is rational [Therefore, 5, a & b are integers, a--2b by b is a rational number]

This contradicts the fact the root 2 is irrational.

The contradiction has arisen because of our incorrect assumption that 5+ root 2 is rational.

Hence, 5+root 2 is irrational.

Hope this helps :D