AM>=GM>=HM. abc=8, a+b+c >=3( abc )^1/3 = 6 a+b+2 >= 8-c 1/a+b+2 + 1/b+c+2 +1/a+c+2 小於等於 1/(8-a) + 1/(8-b) + 1/(8-c) HM = 3/[1/( 8-a ) + 1/( 8-b ) + 1/( 8-c )] 3/[1/( 8-a ) + 1/( 8-b ) + 1/( 8-c )] 小於等於 (1/3)[24-(a+b+c)] 3/[1/( 8-a ) + 1/( 8-b ) + 1/( 8-c )] 小於等於 (1/3)[24-(a+b+c)] 小於等於 6 1/( 8-a ) + 1/( 8-b ) + 1/( 8-c )小於等於1/2
所以1/a+b+2 + 1/b+c+2 +1/a+c+2小於等於1/2 _________________ 想要得到什麼,就必須付出相同的代價...這就是煉金術中所說的"等價交換原則".
|