x=y(=k/2). The maximum product is then (k^2)/4 .

If for two numbers x*y=k(=constant), then their SUM is MINIMUM if

x=y(=root(k)). The minimum sum is then 2*root(k) .

|x| + |y| >= |x+y| (|| stands for absolute value or modulus )

(Useful in solving some inequations)

Product of any two numbers = Product of their HCF and LCM .

Hence product of two numbers = LCM of the numbers if they are prime to each other