The harmonic mean and geometric mean of two values are 6.4 and 8 respectively. the values are

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15 Questions 60 Marks 12 Mins

Given

Geometric mean = 8

Harmonic mean = 6.4

Formula used

Geometric mean = √ab

Harmonic mean = 2ab/(a + b)

Calculation

Let the two number be x and y

√xy = 8

⇒ xy = 64 ---(i)

We also know, 2xy/(x + y) = 6.4

⇒ x + y = 20 ---(ii)

From (i) and (ii)

⇒ 64/y + y = 20

⇒ y2 - 20y + 64 = 0

⇒ y = 4, -16

So, x = 16 and y = 4

∴ The required answer is 4, 16

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