If a be the arithmetic mean and b, c be the two geometric means between any two positive numbers, then $\frac{(b^{3} + c^{3})}{a b c}$ equals

\frac{(a b)^{\frac{1}{2}}}{c}

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1

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\frac{a^{2} c}{b}

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None of these

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Solution

The correct option is D None of these
Solve by taking values and checking with the options. If we take the numbers as 1 and 8, we would get a = 4.5 and b and c as 2 and 4 respectively. Then $\frac{(b^{3} + c^{3})}{a b c} = 2$ . None of the first three options gives us a value equal to 2. Hence, the correct answer is option (d).

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