证明：a^2/b+b^2/c+c^2/d+d^2/a=(a^2/b)+(b^2/c+c^2/d+d^2/a)≥(a^2/b)+(b+c+d)^2/(c+d+a) (柯西不等式）=a^2/b+(4-a)^2/(4-b) (a+b+c+d=4)=[a^2(4-b)+b(4-a)^2]/[b(4-b)]=(4a^2+16b-8ab)/[b(4-b)]=[(16b-4b^2)+(4a^...