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!
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!