Question

a>b>c,求证b^c2+c^a2+a^b2>b2^c+c2^a+a2^b

Answer 1

题目错了,应该是 b^c2+c^a2+a^b2 < b2^c+c2^a+a2^b!

b^c2+c^a2+a^b2-b2^c-c2^a-a2^b

=b^c2--b2^c+c^a2-a2^b+a^b2-c2^a

=b^c(c-b)+a2(c-b)-a(c2-b2)

=b^c(c-b)+a2(c-b)-a(c+b)(c-b)

=(c-b)(b^c+a2-ac-ab)

=(c-b)(b(c-a)-a(c-a))

=(c-b)(b-a)(c-a)

由题知

(c-b)