Question

prove that 1 ÷ 2-√5 is irrational ​

Answer 1

Answer:

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,our supposition is false.

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

Hence proved.

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