|a|+（|b|/2）-√2√|ab|
=（√|a|）^2+[√|b/2|]^2-2√(|a||b/2|）
=[√|a|）-√|b/2|]^2
≥0,
当√|a|=√|b/2|,即|a|=|b/2|,a=±b/2时,取等号.
所以|a|+（|b|/2）≥√（2√|ab|）,a=±b/2时,取等号.