Answer is: a<=-2 or a>=2

We have,

(a+1)(x^4+ x^2+ 1)=(a-1)(x^2 + x + 1)^2

1) Multiply (x²-1) to both sides:

LHS=(a+1)(x^4+ x^2+ 1) * (x²-1) =(a+1)(x⁶-1)

RHS=(a-1)(x^2 + x + 1)^2* (x²-1) = (a-1)(x^2 + x + 1)(x^2 + x + 1)*(x-1)*(x+1)=(a-1)(x^2 + x + 1)(x³-1)*(x+1)

2) Cancel (x³-1) from both sides.

LHS=(a+1)(x³+1)=(a+1)(x+1)(x²-x+1)

RHS=(a-1)(x^2 + x + 1)*(x+1)

3)Cancel (x+1)

LHS=(a+1)(x²-x+1)

RHS=(a-1)(x^2 + x + 1)

4) Cross multiply to get terms of 'a' on one side and 'x' on another. And then apply componendo-dividendo, to get

a = x+1/x

or, x²-ax+1=0

5) For x to be real, the quadratic eq should have a non-negative D.

D=b²-4ac=a²-4>=0

Thus, a<=-2 or a>=2

1. Sit in a straight, comfortable chair in a well-lighted place with plenty of freshly sharpened pencils.

2. Read over the assignment carefully, to make certain you understand it.

3. Walk down to the vending machines and buy some coffee to help you concentrate.

4. Stop off at another floor, on the way back and visit with your friend from class. If your friend hasn't started the paper yet either, you can both walk to the nearby cafe and buy a hamburger to help you concentrate. If your friend shows you his paper, typed, double-spaced, and bound in one of those irritating see-through plastic folders, drop him.

5. When you get back to your room, sit in a straight, comfortable chair in a clean, well-lighted place with plenty of freshly sharpened pencils.

6. Read over the assignment again to make absolutely certain you understand it.

7. You know, you haven't written to that kid you met at camp since fourth grade. You'd better write that letter now and get it out of the way so you can concentrate.

8. Go look at your teeth in the bathroom mirror.

9. Listen to one side of your favourite tape and that's it-- I mean it! As soon as it's over you are going to start that paper.

10. Listen to the other side.

11. Rearrange all of your CDs into alphabetical order.

12. Phone your friend on the other floor and ask if he's started writing yet. Exchange derogatory remarks about your teacher, the course, the university, and the world at large.

13. Sit in a straight, comfortable chair in a clean, well-lighted place with plenty of freshly sharpened pencils.

14. Read over the assignment again; roll the words across your tongue; savour its special flavour.

15. Check the newspaper listings to make sure you aren't missing something truly worthwhile on TV. NOTE: When you have a paper due in less than 12 hours, anything on TV from 'Rahul Dulhaniyan Le Jayenge' to every Zee or Sony soap is truly worthwhile.

16. Phone your friend on the third floor to see if he was watching. Discuss the finer points of the plot.

17. Go look at your tongue in the bathroom mirror.

18. Look through your roommate's book of pictures from home. Ask who everyone is.

19. Sit down and do some serious thinking about your plans for the future.

20. Open your door and check to see if there are any mysterious, trench-coated strangers lurking in the hall.

21. Sit in a straight, comfortable chair in a clean, well-lighted place with plenty of freshly sharpened pencils.

22. Read over the assignment one more time, just for the heck of it.

23. Scoot your chair across the room to the window and watch the sunrise.

24. Lie face down on the floor and scream at the top of your lungs.

25. Leap up and write the paper.

26. Type the paper.

27. Complain to everyone that you didn't get any sleep because you had to write the paper. :D

1) If you want to go for the IIT brand, you'd better take mining in IIT KGP...

• I've heard that its course is not that good (dunno what that means exactly) but once you pass out shining, then there's a lot of money..
• Again, there may be a place issue with KGP, about which you better ask from an IIT KGPian
• Although Brach change is not a relaible option, but you can talk to some KGPian to know how easy/diff it is to get a BC there.. But it's not going to be easy.
• If you have preference to MBA/IAS in the future, better go for colllege than branch

2) If you rather want to go for the branch, mech @ ITBHU is very good..

• Mech is a gr8 branch
• ITBHU is among the top 15 (maybe in top 10)
• And, I personally feel that you need to take a branch that you can study for 4 years.

Hope that helps.. :)

I'd prefer Pilani Chem anytime.. unless you have a strong inclination towards CS..

And packages aren't a proper parameter that helps in the judgement of a branch and college, it depends on the students intake that year..

And more importantly, a good college provides a better environment for one to develop himself.. and BITS Pilani is a great college..

Hope that helps.. :)

 I too got Roorkee... Well, I think u shud opt for 'A' course.. the one with C++ bcoz:

1)C++ is what we have in 1st year.. Not Java.. (Unless you are a CS guy, then you'll have C++ in 1st and Java in 2nd/3rd year).. So it'll also help you maintain CGPA..

2)C++ is the most fundamental.. an ideal case is that 1stly learn C++ and then Java.. Although one can learn Java b4 C++, but the other very is very much easier..

though seniors can help better..