Question

prove that 9-2√2 is irrational​

Answer 1

Answer:

Step-by-step explanation:

9-2√2=a/b

-√2= a-9/2b

Since a-9/2bis rational

We know that √2 is irrational

So 9-2√2 is irrational

Answer 2

Step-by-step explanation:

Let us assume that 9-2√2 is rational

let,9-2√2=a/b(such that a and b are coprime)

9-2√2=a/b

-2√2=a/b-9

2√2=9-a/b

2√2=9b-a

√2=9b-a/2b(where a and b are integers)

since 9b-a/2b is rational therefore .√2is rational

But it contradicts the fact that √2 is irrational

This contradiction has arisen due to our incorrect assumption that 9-2√2 is rational

Thus we conclude that 9-2√2 is irrational

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