Question

prove that p+q is irrerational wherep,q are primes​

Answer 1

Answer:

Now x, x², p, q and 2 are all rational, and rational numbers are closed under subtraction and division. So (x² - p - q) / 2 is rational. But since p and q are both primes, then pq is not a perfect square and therefore √(pq) is not rational. But this is a contradiction.

please mark me as brainliest

Answer 2

Answer:

= √p + √q = a/b

∴ By Squaring on Both sides,

= (√p + √q)² = (a/b)²

= (√p)² + (√q)² + 2√pq = a²b²

= p + q + 2√pq = a²/b²

= p + q + 2√pq = a²/b²

= a²b² - p - q = 2√pq

∵ LHS ≠ RHS

∴ p, q are Prime Numbers

Hence, pur Assumption that √p+√q is a Rational Number is False (or) Wrong.

∴ √p+√q is Irrational.