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题目(2014届江苏省泰州市高三上学期期末第14题)已知函数f(x)=3x+a和g(x)=3x+2a的零点都在区间(b,c)内,则a2+2ab+2ac+4bc b2-2bc+c2的最小值为.这是一道得分率非常低的难题,待求表达式含三个变量,但三个变量之间并没有直接的等量关系,所以消元是较困难的,那只得硬着头皮去求三元函数的最值问题了,这可是很困难的一件事,在短时间内很难完成,绝大部分考生都知难而退.当然,也有成功的,估计最小值肯定是一个与三个变量无关的常数,既然不能消元,那我们只得减
(2014 session of the third high school in Taizhou, Jiangsu end of the first 14 questions) Known function f (x) = 3x + a and g (x) = 3x +2a zero points in the interval (b, c), then a2 + 2ab + 2ac + 4bc The minimum value of b2-2bc + c2 is 0. This is a very low scoring problem. The expression to be evaluated contains three variables, but there is no direct equivalence between the three variables Elimination is more difficult, it would only bite the bullet to seek the most valuable issue of the ternary function, but this is a very difficult thing, difficult to complete in a short time, the vast majority of candidates are knowledgeable. Of course, there are also successes. The estimated minimum must be a constant that has nothing to do with the three variables. Since we can not eliminate them, we only have to subtract