CMO 1988 Problem 4

(1) Let $a,b,c$ be positive real numbers satisfying $(a^2+b^2+c^2)^2>2(a^4+b^4+c^4)$ . Prove that $a,b,c$ can be the lengths of three sides of a triangle respectively. (2) Let $a_1,a_2,\dots ,a_n$ be $n$ ( $n>3$ ) positive real numbers satisfying $(a_1^2+a_2^2+\dots +a_n^2)^2>(n-1)(a_1^4+ a_2^4+\dots +a_n^4)$ . Prove that any three of $a_1,a_2,\dots ,a_n$ can be the lengths of three sides of a triangle respectively.