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प्रश्न
Prove that \[2\sqrt{3} - 1\] is an irrational number.
उत्तर
Let us assume that \[2\sqrt{3} - 1\] is rational .Then, there exist positive co primes a and b such that
`2sqrt3-1=a/b`
`2sqrt3=a/b+1`
`sqrt 3=(a/b+1)/2`
`sqrt3=(a+b)/(2b)`
This contradicts the fact that `sqrt3` is an irrational
Hence `2sqrt3-1` is irrational
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