If the arithmetic mean and harmonic mean of two distinct positive numbers is 16 and 4 respectively, then the geometric mean of the two numbers is

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Solution

The correct option is D
8

The arithmetic mean , harmonic mean , geometric mean of two distinct numbers a and b is given by $\frac{(a + b)}{2}, \frac{2 a b}{(a + b)} a n d (a b)^{(1 / 2)}$ respectively .

$\frac{(a + b)}{2} = 16 \frac{2 a b}{(a + b)} = 4 S o, (a b)^{(1 / 2)} = 8$

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If the arithmetic mean and harmonic mean of two distinct positive numbers is 16 and 4 respectively, then the geometric mean of the two numbers is

The correct option is D 8 The arithmetic mean , harmonic mean , geometric mean of two distinct numbers a and b is given by (a+b)2,2ab(a+b) and (ab)(1/2) respectively . (a+b)2=162ab(a+b)=4So,(ab)(1/2)=8

The correct option is D
8

The arithmetic mean , harmonic mean , geometric mean of two distinct numbers a and b is given by $\frac{(a + b)}{2}, \frac{2 a b}{(a + b)} a n d (a b)^{(1 / 2)}$ respectively .

$\frac{(a + b)}{2} = 16 \frac{2 a b}{(a + b)} = 4 S o, (a b)^{(1 / 2)} = 8$