Min $x^5+3\sqrt{3}\;y^5+\sqrt{3}z^5+t^5-15xyzt$
 

Cho $x,y,z,t>0.$Tim Min $x^5+3\sqrt{3}\;y^5+\sqrt{3}z^5+t^5-15xyzt$

A.M G.M Inequality

$\displaystyle x^5+3\sqrt{3}y^5+\sqrt{3}z^5+t^5+27\geq \bigg(x^5\cdot 3\sqrt{3}y^5\cdot\sqrt{3}z^5\cdot t^5\cdot 27 \bigg)^{\frac{1}{5}}=15xyzt$

$\displaystyle x^5+3\sqrt{3}y^5+\sqrt{3}z^5+t^5-15xyzt\geq -27$

Dấu bằng xảy ra khi $\displaystyle x^5=3\sqrt{3}y^5=\sqrt{3}z^5=t^5=27.$