不等式求最大值.以知4m^2-2mc+c^2=12,求2m+c 最大值是多少?注意符号的方向。

(2m+c)^2=4m^2+4mc+c^2=12+6mc
12=4m^2-2mc+c^2>=2mc
mc2m+c

(2m)^2-2mc+c^2=12≥2*2m*c-2mc=4mc-2mc=2mc
12≥2mc
2mc≤(2m+c)^2/4
∵12≥2mc
(2m+c)^2≤12*4=48
2m+c≤√48=4√3