Question

Prove that (x + Vy is irrational, where x and y are primes.​

Answer 1

Step-by-step explanation:

Let us assume that √x and √y are irrational no.

⇒√x+√y = a/b where '' a and b'' are integers , b ≠0

⇒ √x = a/b-√y -----(1)

now squaring both side we get

⇒ x = ( a/b -√y )² = a²/b² +y -2ab√y

on solving we get

2a/b√y = a²/b²+y -x

⇒ on solving the equation we get

√y = xb²+a²-b²y/2ab

Irrational = Rational

Thus it is not possible ,so our assumption is wrong

Hence √x+√y is irrational.