已知正数a、b、c满足3a+4b+5c=1,求1/(a+b)+1/(b+c)+1/(c+a)的最小值

设a+b=x,b+c=y,a+c=z,则x+3y+2z=3a+4b+5c=1由柯西不等式,(1/x+1/y+1/z)(x+3y+2z)≥(1+根号3+根号2)²=6+2*根号2+2*根号3+2*根号6,即1/(a+b)+1/(b+c)+1/(c+a)≥6+2*根号2+2*根号3+2*根号6x=根号3*y=根号2*z时等号...