在等式4x+9y＝m中，x＞0，y＞0，若x+y的最小值为56，则m的值为．

Question

(4)/(x)+(9)/(y)＝m中，x＞0，y＞0，若x+y的最小值为(5)/(6)，则m的值为______．(4)/(x)44xx(9)/(y)99yy(5)/(6)，则m的值为______．(5)/(6)5566

Answer 1

∵x＞0，y＞0，∴x+y=(1)/(m)((4)/(x)+(9)/(y))(x+y)=(1)/(m)(13+(9x)/(y)+(4y)/(x))≥(1)/(m)(13+2√((9x)/(y)•(4y)/(x)))=(25)/(m)，当且仅当(x)/(y)＝(2)/(3)＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． (1)/(m)111mmm((4)/(x)444xxx+(9)/(y)999yyy)(x+y)=(1)/(m)(13+(9x)/(y)+(4y)/(x))≥(1)/(m)(13+2√((9x)/(y)•(4y)/(x)))=(25)/(m)，当且仅当(x)/(y)＝(2)/(3)＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． (1)/(m)111mmm(13+(9x)/(y)9x9x9xyyy+(4y)/(x)4y4y4yxxx)≥(1)/(m)(13+2√((9x)/(y)•(4y)/(x)))=(25)/(m)，当且仅当(x)/(y)＝(2)/(3)＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． ≥(1)/(m)111mmm(13+2√((9x)/(y)•(4y)/(x))

(9x)/(y)•(4y)/(x)

(9x)/(y)•(4y)/(x)(9x)/(y)9x9x9xyyy•(4y)/(x)4y4y4yxxx)=(25)/(m)，当且仅当(x)/(y)＝(2)/(3)＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． (25)/(m)252525mmm，当且仅当(x)/(y)＝(2)/(3)＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． (x)/(y)xxxyyy＝(2)/(3)222333＞0时取等号．
∴(25)/(m)＝(5)/(6)，解得m=30．
故答案为30． (25)/(m)252525mmm＝(5)/(6)555666，解得m=30．
故答案为30．