Question

Show that 2-√5 is irrational

Answer 1

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let 2-√5 be irrational ( where p and q are co-primes)
2-√5=p/q
-√5=p/q-2
√5=2-p/q

irrational≠rational.
this is not possible so √5is irrational.

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Answer 2

Answer ... solution..

Let us assume that 2-√5 is rational.

2-√5 = a/b ( b is not =0)

2-a/b=√5

√5=5-a/b=5b-a/b

Since a and b are integers ,we get 2-a/b is rational,and so√5 is rational.

But this contradicts the fact that √5 is irrational .

These contradiction has arisen because of our incorrect assumption that 2-√5 is rational.

So, that we conclude that 2+√5 is irrational.

Step-by-step explanation: