Find the two numbers whose A.M. is 25 and GM is 20.
Let A.M. and G.M. between the two numbers a and b be A and G, respectively.
A = 25
⇒a+b2=25
⇒a+b=50 ..........(i)
Also, G = 20
⇒√ab=20
⇒ab=400 ..........(ii)
Now, putting the value of a in (ii):
⇒(50−b)b=400
⇒b2−50b+400=0
⇒b2−10b−40b+400=0
⇒b(b−10)−40(b−10)=0
⇒(b−10)(b−40)=0
⇒b=10,40
If b = 10, then, a = 400
And, if b = 40, then a = 10
Thus, the two numbers are 10 and 40.