If three non-zero distinct real numbers ...

If three non-zero distinct real numbers form an arithmatic progression and the squares of these numbers taken in the same order constitute a geometric progression. Find the sum of all possible common ratios of the geometric progression.

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If three non-zero distinct real numbers form an arithmatic progression and the squares of these numbers taken in the same order constitute a geometric progression. Find the sum of all possible common ratios of the geometric progression.

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