<s>[INST] Prove or disprove $(a^2+b^2)(b^2+c^2)(c^2+a^2)\leq(a+b)(b+c)(c+a)$ Prove or disprove: 
If $a, b, c \in (0, \infty)$ such that $a^2+b^2+c^2=3$ then
$$(a^2+b^2)(b^2+c^2)(c^2+a^2)\leq(a+b)(b+c)(c+a).$$
All my attempts to prove inequality have been unsuccessful. Maybe someone has an idea. Thank you very much!
 [/INST] It's wrong! Try $c\rightarrow0^+$ and $a=b\rightarrow\sqrt{1.5}$
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