题目:已知:1≤a-b≤2,且2≤a+b≤4,求4a-2b的范围.对于上述题目,不少同学采用下面的方法求解:由于1≤a-b≤2,2≤a+b≤4,两式相加得3≤2a≤6,即23≤a≤3,6≤4a≤12,两式相减得,0≤b≤32,得-3≤-2b≤0,故3≤4a-2b≤12上面的解法看上去似乎每一步都是合情合理的,但实际上答案是错 Title: Known: 1 ≤ ab ≤ 2, and 2 ≤ a + b ≤ 4, find the range of 4a-2b. For the above problem, many students use the following method to solve: As 1 ≤ ab ≤ 2, 2 ≤ a +b≤4, the sum of two formulas is 3≤2a≤6, that is, 23≤a≤3, 6≤4a≤12, the two formulas are subtracted, 0≤b≤32, and -3≤-2b≤0. So the solution above 3 ≤ 4a-2b ≤ 12 seems to be reasonable for every step, but in fact the answer is wrong