Show : P+Q=1⇒ PxQ≤1/4 Answer Please!!

Question

Show : P+Q=1⇒ PxQ≤1/4 Answer Please!!

Answer 1

will prove it by contradiction....

P+Q = 1 is given

Then Q = 1 - P

Assume or Suppose PQ > 1/4.

Then PQ - 1/4 > 0.

P(1-P) - 1/4 > 0

P - P^2 - 1/4 > 0

P^2 - P + 1/4 < 0

4P^2 - 4P + 1 < 0

(2P - 1)(2P -1) < 0

(2P - 1)^2 < 0

this is a contradiction... the square of anything must be positive or zero