Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#2 Re: Help Me ! » Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that: » 2012-07-09 22:22:48

a+b+c=1,prove \;  that\sum \frac{\sqrt{a}}{1-a}\geqslant \frac{3\sqrt{3}}{2};prove:\left ( a+b+c \right )^{3}=\left ( \sum \sqrt[3]{\frac{\sqrt{a}}{1-a}} \ast  \sqrt[3]{\frac{\sqrt{a}}{1-a}} \ast \sqrt[3]{{a^{2}(1-a)^{2}}} \right )^{3}

#3 Re: Help Me ! » Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that: » 2012-07-09 14:13:18

Hi,Thank you,I have proved p=1/2 the inequality is right.
I want to know p=1/3 the inequality is right too? how prove? pln3/2>ln9/8 the inequality is right too?right?

#9 Re: Help Me ! » Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that: » 2012-07-03 01:51:09

Hi;
\frac{3^(2-p)}{2}
Not
3^{\frac{(2-p)}{2}}
thank you!

#10 Re: Help Me ! » Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that: » 2012-07-03 01:29:55

\frac{a^p}{1-a}+\frac{b^p}{1-b}+\frac{c^p}{1-c}\geq \frac{3^(2-p)}{2}

#11 Help Me ! » Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that: » 2012-07-02 20:35:27

hcj73jx
Replies: 28

Help me!!!a>0,b>0,c>0,a+b+c=1,0<p<1,prove that:

a^p/(1-a)+b^p/(1-b)+c^p/(1-c)≥3^(2-p)/2

Board footer

Powered by FluxBB