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Determine the largest area of an isosceles triangle that is enclosed within a unit cube.

What is the answer if the triangle is equilateral?

If x, y, z satisfy:

x + y + z = 12,
1/x + 1/y + 1/z = 2, and
x³ + y³ + z³ = -480,

find x²y + xy² + x²z + xz² + y²z + yz².