Squircles!

Algebra Level 4

A squircle is a mathematical shape with properties between those of a square and those of a circle. A squircle centered at the origin is defined by the equation: \(x^4+y^4 = r^4\)

What is the sum of the squares of the distinct \(x\)-coordinates of the intersections of the graphs: \(x^4+y^4 = 8\) and \(y = \sqrt[4]{-6x^2+16}\)

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