Question

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 1

Correct Answer - Option 1 : 4,16

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 = \(\rm \sqrt{ab}\)

 

Calculation:

Here AM = 10 and GM = 8

So,\(\rm\frac{a + b}{2}\) = 10 

⇒ a + b = 20    ....(1) 

Again , \(\rm \sqrt{ab}\) = 8 

⇒ ab = 64        ....(2)

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