Find the two numbers whose A.M. is 25 and GM is 20.

Asked by Sakshi | 1 year ago |  138

##### Solution :-

Given: A.M = 25, G.M = 20.

G.M = $$\sqrt{ab}$$

A.M = $$\dfrac{(a+b)}{2}$$

So,

$$\sqrt{ab}$$ = 20 ……. (1)

$$\dfrac{(a+b)}{2}$$ = 25……. (2)

a + b = 50

a = 50 – b

Putting the value of ‘a’ in equation (1), we get,

$$\sqrt{(50-b)b}= 20$$

50b – b2 = 400

b2 – 50b + 400 = 0

b2 – 40b – 10b + 400 = 0

b(b – 40) – 10(b – 40) = 0

b = 40 or b = 10

If b = 40 then a = 10

If b = 10 then a = 40

The numbers are 10 and 40.

Answered by Aaryan | 1 year ago

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