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

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 22:56:34
已知x>0y>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>0y>0(2x+3y)(3x+2y)=75求x+y的最小值.2)已知x>0求4x/

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