Find two positive numbers a and b Whose Am =25 and Gm=20
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Step-by-step explanation:
Given: A.M = 25, G.M = 20.
G.M = √ab
A.M = (a + b)/2
So, √ab = 20 …….
(
1) (a + b)/2 = 25…….
(2) a + b = 50 a = 50 – b
Putting the value of ‘a’ in equation (1),
we get, √[(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.
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