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