证：
(x²+4)/√(x²+2)
=(x²+2+2)/√(x²+2)
=√(x²+2)+2/√(x²+2)
由均值不等式得,当√(x²+2)=2/√(x²+2)时,即当x=0时,√(x²+2)+2/√(x²+2)有最小值2√2
因此(x²+4)/√(x²+2)≥2√2