Q. 74.3( 8 Votes )

Prove that <span

Answer :

Assume that 23 - 1 is rational
23 = a/b , where a and b are integers .
23 = a/b + 1
2√3 = a/b + b/b
3 = (a + b) / 2b
we know that a, b, and 2 are integers and they are also rational {i.e RHS is rational}
therefore3 will be rational.
but we know that3 is irrational.
there is a contradiction
so, 23 - 1 is an irrational number.


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