Question

prove that 1/(2+√3) is an irrational number​

Answer 1

Answer:

Proved 1/(2+√3) is irrational

Step-by-step explanation:

By contradicting method,

Let 1/(2+√3) is rational

Therefore, 1/(2+√3) = p/q

...(rational number is in p/q where q is not equal to 0)

=> 1/(2+√3) = p/q

=> q = 2p + √3p

=> (q - 2p)/p = √3

We see that

√3 is irrational

Rational = Irrational

This can not possible in rational number.

Which emplies that,

1/(2+√3) is irrational number.

Thank you,

Solved by

Aaditya Singh

NOTE : I can't copy and paste any answer this is my real time answer.