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Tushar Watts Grade: 12
        

Show that the least natural number a for which x + ax -2 > 2  for all x belonging to (0,infinity) is 2.

7 years ago

Answers : (1)

Ramesh V
70 Points
										

This can be simply solved using A.M > G.M


as a,x are positive(given conditions0


let the elements be : x/2 , x/2 , a/x2


so A.M = 1/3*[ x/2 + x/2 + a/x2 ]


   G.M = [ x/2 * x/2 * a/x2 ]1/3


so its, x + a/x2 > 3.(a/4)1/3


     as x + a/x2 > 2, it is clear that


        3.(a/4)1/3   >= 2


          a >= 32/27


since a is natural number, min. possible is 2


--


regards


Ramesh

7 years ago
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