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Answer this for me ,,first who answered ,he would be the brainliest |
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Answer» n:If possible , LET 3 be a rational number and its simplest form be ba then, a and b are integers having no common factor other than 1 and b =0.Now, 3 = ba ⟹3= b 2a 2 (On SQUARING both SIDES )or, 3b 2 =a 2 .......(i)⟹3 divides a 2 (∵3 divides 3b 2 )⟹3 divides aLet a=3c for some integer cPutting a=3c in (i), we getor, 3b 2 =9c 2 ⟹b 2 =3c 2⟹3 divides b 2 (∵3 divides 3c 2 )⟹3 divides aThus 3 is a common factor of a and bThis contradicts the fact that a and b have no common factor other than 1.The contradiction arises by ASSUMING 3 is a rational.Hence, 3 is irrational.2 nd partIf possible, Let (7+2 3 ) be a rational number.⟹7−(7+2 3 ) is a rational∴ −2 3 is a rational.This contradicts the fact that −2 3 is an irrational number.Since, the contradiction arises by assuming 7+2 3 is a rational.Hence, 7+2 3 is irrational.Proved. |
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