Question

The arithmetic mean and geometric mean of two positive numbers are 10 and 10 respectively. Determine the numbers.​

Answer 1

Answer:

The numbers are 10 and 10 respectively.

Step-by-step explanation:

Let the two positive numbers be a and b respectively.

Now,

• ( a + b )/2 = 10
• a + b = 2 × 10
• a + b = 20

Then,

• √ab = 10
• ab = 10²
• ab = 100

We know that,

• ( a - b )² = ( a + b )² - 4ab
• ( a - b )² = ( 20 )² - 4 × 100
• ( a - b )² = 400 - 400
• ( a - b )² = 0
• a - b = 0
• a = b ...1

Now,

• a + b = 20

From 1

• a + a = 20
• 2a = 20
• a = 20/2
• a = 10

Now, we know that a = b from 1

Therefore,

• b = 10

∴ The numbers are 10 and 10 respectively.

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