$a^{4}$+ $b^{4}$+ $c^{4}$+ $d^{4}$ $≥4abcd^{}$
⇔$a^{4}$-$2a^{2}b^{2}$+$b^{4}$+$c^{4}$-$2c^{2}d^{2}$+$d^{4}$+$2a^{2}b^{2}$+$2c^{2}d^{2}$$-4abcd^{}$ $≥0^{}$
⇔($a^{2}$+ $b^{2}$)$^{2}$+( $c^{2}$-$d^{2}$)$^{2}$+$+2(ab-cd)^{2}$ $\geq$ $0^{}$
$Dấu^{}$ $"="^{}$ $xảy^{}$ $ra^{}$ $khi^{}$ $a=b=c=d^{}$