Question

The arithmetic mean of x and y is 10 and their geometric mean is 8, what is the value of x and y?

Answer 1

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Answer 2

Given:

The arithmetic mean of x and y is 10 and their geometric mean is 8

To find:

What is the value of x and y?

Solution:

From given, we have,

The arithmetic mean of x and y is 10 and their geometric mean is 8

Now consider,

The arithmetic mean of x and y is 10

⇒ (x + y)/2 = 10

x + y = 20 ...... (1)

y = 20 - x ...... (2)

The geometric mean of x and y is 8

⇒ √xy = 8

square on both the sides,

xy = 8²

xy = 64...... (3)

substitute the value of equation (2) in the equation (3)

x (20 - x) = 64

20x - x² = 64

x² - 20x + 64 = 0

(x - 4) (x - 16) = 0

x = 4, 16

when x = 4,

xy = 64 ⇒ y = 64/x ⇒y = 64/4 ⇒ y = 16

∴ y = 16

when x = 16,

xy = 64 ⇒ y = 64/x ⇒y = 64/16 ⇒ y = 4

∴ y = 4

The values of x and y are 4 and 16