Question

Prove that 2-v3 is irrational, given that v3 is irrational​

Answer 1

given

2-√3 is irrational

to prove

2-√3 is irrational

solution

let us consider 2-√3 as rational

⇒ 2-√3 =a/b(where a  and b are integers)

⇒-√3=a/b-2

⇒-√3=a/b-2

⇒squaring on both sides

we get

3=a2-2b/b

⇒a2-2b/3b

⇒it is in the form of p/q but

contradicts because √3 is irrational

hence proved

hope it helps

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