已知x1,x2,x3均为正数,且x1+x2+x3=1,求证x1^2\(x1+x2)+x2^2\(x2+x3)+x3^2\(x1+x_数学解答

已知x1,x2,x3均为正数,且x1+x2+x3=1,求证x1^2\(x1+x2)+x2^2\(x2+x3)+x3^2\(x1+x3)≥1\2

人气：138 ℃　时间：2020-04-15 08:31:07

解答

柯西不等式[x1^2\(x1+x2)+x2^2\(x2+x3)+x3^2\(x1+x3)]*[(x1+x2)+(x2+x3)+(x1+x3)]>=[根号(x1^2\(x1+x2)*(x1+x2))+根号(x2^2\(x2+x3)*(x2+x3))+根号(x3^2\(x3+x1)*(x3+x1))]^2=[x1+x2+x3]^2=1而(x1+x2)+(x2+x3)+(x1+x...