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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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