If the arithmetic mean of two positive numbers \( a \& b(ab) \) is ...

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If the arithmetic mean of two positive numbers \( a \& b(ab) \) is twice their geometric mean, then \( a \) : \( b \) is:
(A) \( 2+\sqrt{3}: 2-\sqrt{3} \)
(B) \( 7+4 \sqrt{3}: 1 \)
(C) \( 1: 7-4 \sqrt{3} \)
(D) \( 2: \sqrt{3} \)
\( \mathrm{P} \)
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