已知x>0 y>0 (2x+3y)(3x+2y)=75 求x+y的最小值.2）已知x>0 求4x/(x^2+5)的最值

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已知x>0 y>0 (2x+3y)(3x+2y)=75 求x+y的最小值.2）已知x>0 求4x/(x^2+5)的最值
已知x>0 y>0 (2x+3y)(3x+2y)=75 求x+y的最小值.
2）已知x>0 求4x/(x^2+5)的最值

已知x>0 y>0 (2x+3y)(3x+2y)=75 求x+y的最小值.2）已知x>0 求4x/(x^2+5)的最值
75＝(2x+3y)(3x+2y)
　　＝6x＾2＋13xy＋6y＾2
　　＝6（x＋y）＾2＋xy＞＝24xy＋xy＝25xy
xy＜＝3
x＋y＞＝2vxy＝2v3
最小值2v3

let d =x+y
(2x+3y)(3x+2y)=75
(2(x+y) +y) ( 2(x+y) +x ) =75
6(x+y)^2 + xy =75
6d^2 +x(d-x) =75
(12d)d'+ (d-x) + x(d' -1) =0
(12d+x) d' = 2x-d
d' = 0
=> x= d/2
y=d/2
(2x+3y)(3x+2y)=75
(d+3d/2)(3d/2 +d) =75
25d^2/4 =75
d^2 = 12
d =2√3
ie
min x+y = 2√3

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