Question

Given that V3 is irrational, prove that 4-2V3 is also irrational.​

Answer 1

Given:

√3 is irrational

To prove:

4-2√3 is also irrational

Proof:

Let 4-2√3 be a rational number equal to a

⇒   4-2√3 = a

⇒   -2√3 = a-4

⇒   √3 =  { (a-4) / (-2) }

⇒   √3 = (-a+4)/2   or   (4-a)/2

   But Irrational ≠ Rational

⇒ L.H.S. ≠ R.H.S.

Hence 4-2√3 is irrational

                 ***************END OF SOLUTION***************