比較大小難題

M - N= (a²b + b²c + c²a) - (c²b + a²c + b²a)= (a² - c²)b + (b² - a²)c - (b² - a² + a² - c²)a= (a² - c²)(b - a) + (b² - a²)(c - a)= (a - c)(b - a) (a + c) - (a - c)(b - a) (b + a)= (a - c)(b - a) (a + c - (b + a))= (a - c)(b - a) (c - b)= (+) ( - ) ( - )= +> 0故 M > N

Assuming that a, b and c are all positive.
Since a > b
Multiplying both side by ab, we get a^2b > ab^2...............(1)
Similarly,
b > c
Multiply both side by bc, we get b^2c > bc^2...............(2)
Similarly,
a > c
so a^2c > ac^2.....................(3)
(1) + (2) - (3), we get
a^2b + b^2c - a^2c > ab^2 + bc^2 - ac^2
Rearranging we get
a^2b + b^2c + ac^2 > ab^2 + bc^2 + a^2c
that is M > N.