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一、不等思等,产生灵感例1 若a,b,c均为正数,且a+b+c=abc,则a~n+b~n+c~n(n＞1,n∈N)的最小值是()(A)3((3~n)~(1/3~n))(B)3(C)9~(1/3)(D)3((3~n)~(1/3~n))[注释]:当我们第一遍读完全题以后,有点儿惘然不知所措。已知条件与结论中的四个选项难以挂起来。仔细观察,题中a,b,c所处位置是对称的,正是对称性这一隐含条件的刺激,可大胆地猜想:当a=b=c时,即3a=a~3,a=3~(1/3)时,取得最小值,且最小值为3(1~(1/3))~n=3 3((3~n)~(1/3~n)),马上可选(A)。
One, not thinking, etc., to create an inspiration example 1 If a, b, c are all positive, and a+b+c=abc, then a~n+b~n+c~n(n>1,n∈) The minimum value of N) is ()(A)3((3~n)~(1/3~n))(B)3(C)9~(1/3)(D)3((3~n )~(1/3~n)) [comment]: When we read the complete question for the first time, it was a bit overwhelmed. The four options in the known conditions and conclusions are difficult to hang. Carefully observe that the positions of a, b, and c in the question are symmetrical. It is the stimulation of the implicit condition of symmetry that can be conjectured: When a=b=c, ie 3a=a~3,a When =3~(1/3), the minimum value is obtained, and the minimum value is 3(1~(1/3))~n=3 3((3~n)~(1/3~n)), immediately Optional (A).