Question

若a>b>c,求证bc^2+ca^2+ab^2＜cb^2＋ac^2＋ba^2

Answer 1

c^2+ca^2+ab^2-cb^2-ac^2-ba^2

=a^2(c-b)+a(b^2-c^2)+bc(c-b)

=(c-b)(a^2-ab-ac+bc)

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

因为a>b>c

∴c-b0

a-c>0

∴(c-b)(a-b)(a-c)