Maximum value 1

Algebra Level 4

a4+b4+c4+abc(a+b+c)k(ab+bc+ca)2\large { a }^{ 4 }+{ b }^{ 4 }+{ c }^{ 4 }+abc\left( a+b+c \right) \ge k{ \left( ab+bc+ca \right) }^{ 2 }

Find the maximum value of kk such that the inequality above holds true with all real values of a,a, b,b, and c.c.

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