The harmonic mean of two positive real numbers is 4. Their arithmetic mean A and their geometric mean G satisfy the relation $2 A + G^{2} = 27.$ Find the two numbers.

4 and 4

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2 and 6

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3 and 6

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5 and 10/3

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Solution

The correct option is C 3 and 6
$H M = \frac{2 a b}{a + b} = 4$
$G M = \sqrt{a b}$
and $A M = \frac{a + b}{2}$
Now, solve through options.

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The harmonic mean of two positive real numbers is 4. Their arithmetic mean A and their geometric mean G satisfy the relation 2A+G2=27. Find the two numbers.

The correct option is C 3 and 6HM=2aba+b=4 GM=√ab and AM=a+b2 Now, solve through options.

The harmonic mean of two positive real numbers is 4. Their arithmetic mean A and their geometric mean G satisfy the relation $2 A + G^{2} = 27.$ Find the two numbers.

The correct option is C 3 and 6
$H M = \frac{2 a b}{a + b} = 4$
$G M = \sqrt{a b}$
and $A M = \frac{a + b}{2}$
Now, solve through options.