Question

1
28. Prove that 1/ 2-√5
is an irrational number.​

Answer 1

Step-by-step explanation:

Let 1/2-√5 is a rational number.

A rational number can be written in the form of p/q where p,q are integers.

1/2-√5=p/q

1/2-p/q=√5

√5=(q-2p)/2q

If p,q are integers then (q-2p)/2q is a rational number.

Then,√5 is also a rational number.

But this contradicts the fact that √5 is an irrational number.

So,supposition is false.

Therefore,1/2-√5 is an irrational number