If AM and GM  of two positive number a and b are  10 and 8 respectively. Find the numbers .

  1. 4,16
  2. 10,10
  3. 12,8
  4. 2, 32

Answer (Detailed Solution Below)

Option 1 : 4,16
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Detailed Solution

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Concept:

If A is the arithmetic mean of numbers a and b and is given by ⇔ A =  (a + b)/2

If G is the geometric mean of the numbers a and b and is given by  ⇔ G = 

Calculation:

Here AM = 10 and GM = 8

So, = 10 

⇒ a + b = 20    ....(1) 

Again ,  = 8 

⇒ ab = 64        ....(2)

After solving both equation, we get a = 4, b = 16 or a = 16, b = 4

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