If variables a, b, c, and d are positive numbers and a + b + c + d = 1,
Can I find the maximum of the expression below?
ab + cd
and how can I reach that?
2026-03-27 21:23:49.1774646629
Given sum of 4 variables as a constant, how to maximize the sum of products?
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Hint:$${(a+b+c+d)}^2-4ab-4cd={(a-b)}^2+{(c-d)}^2+2(ac+bd+ad+bc)\ge 0$$