Recurring Recurrence

Algebra Level 5

Find \(ax^5 + by^5\) if the real numbers \(a, b, x\) , and \(y\) satisfy the equations \[ax + by = 3\]\[ax^2 + by^2 = 7\]\[ax^3 + by^3 = 16\]\[ax^4 + by^4 = 42\]

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