# The answer is... close to 1

Algebra Level 4

Let $${ x }_{ 1 }, { x }_{ 2 }, { x }_{ 3 }, { x }_{ 4 }, { x }_{ 5 }, { x }_{ 6 }$$ be real numbers such that $${ x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }+{ x }_{ 4 }+{ x }_{ 5 }+{ x }_{ 6 }=0$$ and $${ x }_{ 1 }^{ 2 }+{ x }_{ 2 }^{ 2 }+{ x }_{ 3 }^{ 2 }+{ x }_{ 4 }^{ 2 }+{ x }_{ 5 }^{ 2 }+{ x }_{ 6 }^{ 2 }=6$$. Find the maximum value of $${ x }_{ 1 }{ x }_{ 2 }{ x }_{ 3 }{ x }_{ 4 }{ x }_{ 5 }{ x }_{ 6 }$$.