For positive real $a,b,c>0$ show that
$$abc(a+b+c)≤a^3b+b^3c+c^3a.$$
I am told that I should apply Cauchy-Schwarz, but it isn't entirely obvious to me, how I could do that in this case. Any help would be appreciated!
For positive real $a,b,c>0$ show that
$$abc(a+b+c)≤a^3b+b^3c+c^3a.$$
I am told that I should apply Cauchy-Schwarz, but it isn't entirely obvious to me, how I could do that in this case. Any help would be appreciated!