Inequalities: x(x+1)(x+2)(x+3) >= -1, (ab+bc+ca)^2 >= 3abc(a

[xwrathbringerx]

a) Prove that the inequality x(x+1)(x+2)(x+3) >= -1 holds for all real numbers x.

b) Prove that (ab+bc+ca)^2 >= 3abc(a+b+c) holds for all real numbers a, b and c

 

[tkhunny]

Re: Inequalities

a) What do we get to use? The first derivative shows easily the minimum to be -1 in two locations. Can we do that?