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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.`
8 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
```
8 years ago
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