For positive integer numbers, so $\min\{\frac{c}{a},\frac{c}{b}\}+\lfloor\frac{c}{a}\rfloor\lfloor\frac{c}{b}\rfloor\geqq c\lfloor\frac{c}{ab}\rfloor$

score 408 · Answer 14 · 2026-03-26 07:52:43

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Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Published on 26 Mar 2026 - 7:52

score 59 · Answer 15 · 2019-07-14 18:58:22

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Show that $\frac1{\sqrt a}e^{-\frac{b^2}{8a}}$ is bounded

Published on 14 Jul 2019 - 18:58

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For positive integer numbers, so $\min\{\frac{c}{a},\frac{c}{b}\}+\lfloor\frac{c}{a}\rfloor\lfloor\frac{c}{b}\rfloor\geqq c\lfloor\frac{c}{ab}\rfloor$

Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Show that $\frac1{\sqrt a}e^{-\frac{b^2}{8a}}$ is bounded

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