Please help it's urgent
Ch - Real Numbers
Class 10th
Don't even try to post irrevalent answers otherwise your 10 answers will be reported
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First, we'll assume that p and q is rational , where p and q are distinct primes
p+q=x, where x is rational
Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides.
(p+q)2=x2
p+2pq+q=x2
2pq=x2−p−q
pq=2(x2−p−q)
Now, x, x2, p, q, & 2 are all rational, and rational numbers are closed under subtraction and division.
So, 2(x2−p−q) is rational.
But since p and q are both primes, then pq is not a perfect square and therefore pqis not rational. But this is contradiction
Original assumption must be wrong.
So, p and q is irrational, where p and q are distinct
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