Q.

The harmonic mean of two numbers is 4. Their arithmetic mean is A and geometric mean is G.  If G satisfies 2A+G2=27then the numbers are

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a

1, 13

b

9, 12

c

3, 6

d

4, 8

answer is C.

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Detailed Solution

2aba+b=4,a+b2=A ab=G 2A+G2=27⇒a+b+ab=27 ⇒a+b+2a+b=27 ⇒a+b=9 ⇒ab=18 ⇒the numbers are 3,6
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The harmonic mean of two numbers is 4. Their arithmetic mean is A and geometric mean is G.  If G satisfies 2A+G2=27then the numbers are