Question

prove that 1/2-root 3 is an irrational number

Answer 1

Let us assume to the contrary that 1/2-√3 is rational.

Then, there exist positive co-primes p and q such that,
=) 1/2-√3 =p/q

=) q= p(2-√3)

=)q= 2p-p√3

=) √3= q-2p/-p

=) but this contradicts the fact that, √3 is irrational.

Hence, 1/2-√3 is irrational..


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Answer 2

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