A.M. exceeds G.M. by 2, sum = 20.
Let numbers be (x,y>0). [ \dfrac{x+y}{2}-\sqrt{xy}=2,\quad x+y=20 ] [ 10-\sqrt{xy}=2\implies\sqrt{xy}=8\implies xy=64 ]
[ t^2-20t+64=0\implies(t-16)(t-4)=0 ]
Answer: 4 and 16
11TH•Mathematics•Sequences And Series•Question 5
Overview
The A.M. of two positive integral numbers exceeds their (positive) G.M. by 2 and their sum is 20, find the numbers.
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