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Prove that 2-√3 are irrational

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Prove that 2-√3 are irrational

Posted by Vikas Rai 5 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Riyana D'Cunha 5 years, 4 months ago

Let us assume, to the contrary, that 2-√3 is rational. That is , we can find coprime a and b (b≠0) such that 2-√3= a/b. Therefore 2- a/b= √3 Rearranging this equation, we get √3=2-a/b= 2b-a/b Since a and b are integers, we get 2-a/b is rational, and so √3 is rational. But this contradicts the fact that √3 is rational. This contradiction has arisen because of our wrong assumption that 2- √3 is rational. So, we conclude that 2-√3 is irrational. Hope it works.

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