$Cho$ $ba$ $số$ $thực$ $dương$ $x; y; z$ $thoả$ $mãn$: $4xy+4yz+3xz=3xyz.$ $Chứng$ $minh$ $rằng$: $frac{2(x+y)^{2}}{2x+3y}+ frac{(y+2z)^{2}}{2y+z}+ frac{(2z+x)^{2}}{z+2x}$ $geq$ $24$.

2025-03-23 05:59:03

$Cho$ $ba$ $số$ $thực$ $dương$ $x; y; z$ $thoả$ $mãn$: $4xy+4yz+3xz=3xyz.$ $Chứng$ $minh$ $rằng$: $\frac{2(x+y)^{2}}{2x+3y}+ \frac{(y+2z)^{2}}{2y+z}+ \frac{(2z+x)^{2}}{z+2x}$ $\geq$ $24$.

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