X^3+13a^2X-5aX^2-9a^3
=X^3-a^3-5aX^2+13a^2X-8a^3
=(X-a)(X^2+Xa+a^2)-a(5X^2-13aX+8a^2)
=(X-a)(X^2+Xa+a^2)-a(X-a)(5X-8a)
=(X-a)(X^2+Xa+a^2-5aX+8a^2)
=(X-a)(X^2-4aX+9a^2)
=(X-a)[(X-3a)^2+2aX]
因为X>a>0所以X-a>0
所以X^3+13a^2X-5aX^2-9a^3>0
所以X^3+13a^2X>5aX^2+9a^3