Meeting at 3 3 Points

Algebra Level 2

The curve y = x 3 + 9 x 2 + 72 x y=-x^3+9x^2+72x and the line y = k y=k intersect at 3 3 distinct points. If the x x -coordinates of these 3 3 points form a geometric progression, what is the real number k ? k?

488 488 512 512 500 500 524 524

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