Question

prove that 1/2-√5 is an irrational number

Answer 1

Let us assume to the contrary that 1/2- root 5
Is a rational number
We can find co prime a and b
1/2-root5=a/b
1-root 5=2a/b
root 5=-2a/b
Since a, b, and 2 are integers
So - 2a/b is rational
So also root 5 is rational
This contradicts that root 5 is irrational
This contradiction has arisen bcoz of r incorrect assumption that 1/2-root 5 is rational
Therefore 1/2-root 5 is irrational.