真题呈现(2014年辽宁理科卷第16题)对于c>0,当非零实数a,b满足4a~2-2ab+4b~2-c=0,且使|2a+b|最大时,3/a-4/b+5/c的最小值为多解探究多元条件最值是高考的一个热点之一,代数变形,合理转化,代入消元,配方化简是常见的解题技巧.当中的主元思想,方程观点,函数思想是值得不断琢磨、反复思考的.解法1由4a~2-2ab+4b~2-c=0作配方变形,得5(2a+b)~2+3(2a-3b)~2=8c,(*) For c> 0, when the non-zero real numbers a, b satisfy 4a ~ 2-2ab + 4b ~ 2-c = 0 and maximize | 2a + b | / a-4 / b + 5 / c is the minimum value of multiple solutions to explore the maximum value of multiple conditions is one of the hottest college entrance examination, algebra deformation, rational conversion, substitution elimination, formula simplification is a common problem-solving skills. (2a + b) ~ 2 + 3 from the formula of 4a ~ 2-2ab + 4b ~ 2-c = 0 for the solution of the main element, the concept of equation and the idea of ​​function are worth pondering and thinking repeatedly. (2a-3b) to 2 = 8c, (*)