The harmonic mean of two numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A +G2 = 27. Find the numbers.
Given, HM = 4
∴ AM × HM = GM2∴ A × A = G2 ⇒ G2 = 4A
But it is given 2A + G2 = 27
∴ 2A + 4A = 27 ⇒ 6A = 27⇒ A = 92and G2 = 18∴ a + b2 = 92 and ab = 18⇒ a + b = 9 and ab = 18⇒ a = 6, b = 3, b = 6
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Short Answer Type
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