Saved Bookmarks
| 1. |
Prove that 2-√3 are irrational |
| Answer» 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= √3Rearranging this equation, we get √3=2-a/b= 2b-a/bSince 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. | |