|x²-4x+2|≥x/2
(1)当x²-4x+2≥0,即:x≤2-√2或x≥2+√2时
|x²-4x+2|= x²-4x+2≥x/2
故:x²-9x/2+2≥0
故:x≥4或x≤1/2 (结合x≤2-√2或x≥2+√2)
故:x≥4或x≤1/2
(2) 当x²-4x+2≤0,即:2-√2≤x≤2+√2时
|x²-4x+2|= -(x²-4x+2)≥x/2
故:x²-7x/2+2≤0
故:(7-√17)/4≤x≤(7+√17)/4 (结合2-√2≤x≤2+√2)
故:(7-√17)/4≤x≤2+√2
故:x≥4或(7-√17)/4≤x≤2+√2或x≤1/2