MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12
        

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

10 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

10 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details