If $α, β$ are the zeroes of $x^{2} - (k + 6) x + 2 (2 k - 1)$ , and $α + β = \frac{1}{2} α β$ , what is the value of $k$ ?

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If two positive integers $a$ and $b$ are written as $a = x^{3} y^{2}$ and $b = x y^{3}$ , where $x$ and $y$ are prime numbers, what is the…
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