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Maximum Product for Fixed Sum
For positive numbers $$x$$ and $$y$$ with fixed sum:
$$x+y=S$$
their product is maximum when:
$$x=y=\frac{S}{2}$$
and:
$$xy\leq\frac{S^2}{4}$$
Usage
- Used in algebraic and optimization problems involving a fixed sum.
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Maximum Product for Fixed Sum
For positive numbers $$x$$ and $$y$$ with fixed sum:
$$x+y=S$$
their product is maximum when:
$$x=y=\frac{S}{2}$$
and:
$$xy\leq\frac{S^2}{4}$$
Usage
- Used in algebraic and optimization problems involving a fixed sum.
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