If the A.M of two numbers exceeds their G.M by 2 and the G.M exceeds their H.M by 8/5, then the numbers are

Answers (1)

Solutions :   Let the two numbers be a and b , where a> b.

                      Let their  A.M , G.M and H.M be the respectively A,G and H.

                    Then   A=G+2  and G=H+frac85    or   H=G-frac85.

                   	herefore          AH=G^2Rightarrow (G+2)(G-frac85)=G^2

                 Rightarrow                    G=8=sqrtab

                 	herefore          A=8+2=10=fraca+b2Rightarrow a+b=20   .......(1)

                            (a-b)^2=(a+b)^2-4ab=400-256=144    .......(2)

                 From   (1)   and (2)  We get  ,         a=16,b=4

 

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