If $a,b,c$ are sides of a triangle prove that $$a^4+b^4+c^4<2(a^2b^2+b^2c^2+c^2a^2)$$
2026-04-07 12:48:16.1775566096
Inequality involving side lengths of a triangle
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your inequality is equivalent to $$- \left( c+a+b \right) \left( -c+a+b \right) \left( a-b-c \right) \left( -b+c+a \right) >0$$ this is true since we have that $$a,b,c$$ are sides of a triangle.