1.

If then sum of two positive numbers in constant then show that their product is maximum when they are equal.

Answer»

SOLUTION :Let X and y be two positive numbers such that x + y = C (constant)
then y = c - x
Let `p = xy = x(c- x) = cx - x^2`
`dp/dx = c - 2x, (d^2p)/dx^2 = - 2 lt 0`
`therefore` p is maximum when `c - 2x = 0 I.e, x = c/2`
if `x= c/2` then `y=c/2`.
`therefore` The two numbers are equal. (Proved)


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