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

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

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Hello Student,
Please find the answer to your question
Let the two numbers be a and b, then
2ab/a + b = 4 ….(1); a + b/2 = A; √ab = G
Also 2A + G2 = 27 ⇒ a + b + ab = 27 ………… (2)
Putting ab = 27 – (a + b) in eqn. (1). We get
54 – 2(a + b)/a + b = 4 ⇒ a + b = 9 then ab = 27 – 9 = 18
Solving the two we gat a = 6, b = 3 or a = 3, b = 6, which are the required numbers.

Thanks
Aditi Chauhan
askIITians Faculty

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