Cho $x,y,z,t>0$ Chứng minh:
$\frac{x+y+z+t}{\sqrt[4]{xyzt}}+\frac{16xyzt}{(x+y)(y+z)(z+t)(t+x)}\geq 5$
Cho $x,y,z,t>0$ Chứng minh:
$\frac{x+y+z+t}{\sqrt[4]{xyzt}}+\frac{16xyzt}{(x+y)(y+z)(z+t)(t+x)}\geq 5$
Cho $x,y,z,t>0$ Chứng minh:
$\frac{x+y+z+t}{\sqrt[4]{xyzt}}+\frac{16xyzt}{(x+y)(y+z)(z+t)(t+x)}\geq 5$
Sử dụng AM-GM:
$VT=\frac{x+y}{2\sqrt[4]{xyzt}}+\frac{y+z}{2\sqrt[4]{xyzt}}+\frac{z+t}{2\sqrt[4]{xyzt}}+\frac{t+x}{2\sqrt[4]{xyzt}}+\frac{16xyzt}{(x+y)(y+z)(z+t)(t+x)}$
$\geq 5\sqrt[5]{\frac{x+y}{2\sqrt[4]{xyzt}}.\frac{y+z}{2\sqrt[4]{xyzt}}.\frac{z+t}{2\sqrt[4]{xyzt}}.\frac{t+x}{2\sqrt[4]{xyzt}}.\frac{16xyzt}{(x+y)(y+z)(z+t)(t+x)}}=5$
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