Question

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

Answer 1

\(\Rightarrow\) A.M = \(\frac{a+ b}{2}\)

\(\Rightarrow\) G.M = √ab

Given A.M=25, G.M = 20. 

⇒ √ab = 20 …….(1)

⇒ \(\frac{a +b}{2} = 25\) ..... (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