Question

i)show that 1/2+√5 is irrational.

help me friend​

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.

HOPE IT HELPS YOU.

Answer 2

Let 1/2+√5 is rational no.

1/2+√5 = p/q

Where p and q are co prime and q ≠0

√5 = p/q - 1/2

In LHS there is Irrational no. and in RHS there is rational no. This is not possible. This contradiction arise due to our wrong assumption. Thus our assumption is wrong and 1/2+√5 is Irrational no.

Hence proved

.

Hope it helps