Question

Prove that 1-2√5 is irrational​

Answer 1

let 1-2root5 is rational .....

then its simplest form let be .. a/b

where a and b is integer ...

A.T.Q

1-2root5= a/b

or 1= a/b +2root5

or 2root5 =1-a/b

or root5 =(b-a)/2b

now here (b-a)/2b should rational Becouse a and b is integer

but this contradict the fact that root5 is irrational. .

therefore our assumption is wrong and

1-2root5 is irrational !