Question

函数y=a/sinx+b/cosx的最小值

函数y=a/sinx+b/cosx的最小值a b是正实数x 在0到90度

Answer 1

解：引进((m*(A/m)^P+n*(B/n)^P)/(m+n))^(1/P)>=((m*(A/m)^p+n*(B/n)^p)/(m+n))^(1/p) (P>p;m,n,A,B>=0)
设 A=a/sinx;B=b/cosx;m=a^(2/3);n=b^(2/3)=1;p=-2
(a/sinx+b/cosx)/(a^(2/3)+b^(2/3))
>=((a^2/A^2+b^2/B^2)/(a^(2/3)+b^(2/3)))^(-1/2)
=(a^(2/3)+b^(2/3))^(1/2)
y>=(a^(2/3)+b^(2/3))^(3/2)