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I am just wondering, is it true that

$$6 \sqrt{-3 t (1+t)+\sqrt{4+12 t\ \ }\ \ }$$

$$\le\left(\frac{3 t (1+t)+\sqrt{4+12 t}}{1+t+t^2}\ \ \right)^{3/2}+4\sqrt{2}(1-t)^{3/2}$$

for all $\displaystyle t\in[0,1]$?

Thanks!

  • 11
    Oh, just what I was wondering too! :)2011-10-19
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    (What I mean is that it might be helpful to provide some context. Is there any reason to believe it to be true?)2011-10-19
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    Since both sides are positive, you can square each side and eliminate some of the roots... and then if you keep squaring it the right way, you can reduce the problem to a polynomial inequality...Which may or may not be easy, but will probably be easier than this.2011-10-19

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