Question

Prove that 2-√5 is an irrarional no.

Answer 1

Hey buddy.....here's your answer....

Let 2-√5 be a rational number,

So, 2-√5=a/b

Where a and b are co-primes

-√5=(a/b)-2

√5= -(a-2b)/b

L.H.S= √5= Irrational number

R.H.S= -(a-2b)/b=Rational number

L.H.S is not equal to R.H.S

This is contradictory.

This contradiction has arisen because of our wrong assumption.

Hence,2-√5 is an irrational number.

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Answer 2

let us assume that 2-√5 is rational

-so we can right it as 2-√5=a/b

where a and b are integers and b not = 0

therefore, 2-√5=a/b

=2-a/b =√5

=2b-a/2b =√5

2b-a/2b is rational so √5 is also rational by LHS=RHS,which contradicts the fact that √5 is irrational

therefore our assumption is wrong

2-√5 IS IRRATIONAL...

HOPE IT HELPS U