X and y are two numbers whose arithmetic mean is 61 and geometric mean is 11

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10 Questions 10 Marks 10 Mins

Given:

Airthmetic mean = Geometric Mean

Formula Used:

Airthmetic mean = (x + y)/2

Geometric Mean = √xy

Where x and y are 2 numbers

Calculation:

Airthemetic Mean = (a + b)/2

Geometric Mean = √ab

According to question:

√ab = (a + b)/2

Squaring both the sides

ab = [(a + b)/2]2

⇒ 4ab = (a + b)2

⇒ 4ab = a2 + b2 + 2ab

⇒ a2 + b2 - 2ab = 0

⇒ (a - b)2 = 0

⇒ a - b = 0

∴ a = b

The correct option is 2 i.e. a = b

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