ANS A [0]
ATLEAST A HINT PLZZ.....
THIS TYPE HAUNTS ME WER WE USE FUNDAMENTALS OF NUMBERS.....
62sorry wrong hint.... :(
:P
I think you will have to take the fdifference ...
21sir,
didnt understandhow will taking diff help.......
then how will u introduce the fact that f(x) = 5 has 4 integrL soln??????
341these kind of problems are well known.
f(x) - 5 = (x-n1) (x-n2)(x-n3)(x-n4) P(x), where P(x) is a polynomial with integer coefficients
If f(n) = 7, then f(n) - 5 = 2 i.e. (n-n1) (n-n2)(n-n3)(n-n4) P(n) = 2
Now the factors of 2 are ±1, ±2. and remember that only one of ±2 can appear on LHS. Also (n-n1), (n-n2), (n-n3), (n-n4) are all distinct. By pigeonhole principle, we must two of the roots equal, but that contradicts the problem condition
21COOL APPROACH PROPHET!!!!!!!!
hey prophet jus didnt get dat last bit.........
how did u prove dat 4 polynomial = 7 has 0 zero roots.........
in short didnt get it frm here on,
"remember that only one of ±2 can appear on LHS. Also (n-n1), (n-n2), (n-n3), (n-n4) are all distinct."
21i read the pigeonhole principle.... got it...... but how did u apply it to our situation????
341The numbers 1, -1 and 2 (or -2) are to be assigned to n-n1, n-n2, n-n3 and n-n4. So some two of them will be equal say n-n2 and n-n4. This means n2 = n4. But that is forbidden.
21why do you say only one out of
+2 and -2 has to be assigned????
i m sorry if this que sounds a lil dumb....
11hello mr prophet i want to ask you something many terms that you use in your proofs i havent even seen or heard them before
are they really in the jee level please reply
21PROPHET SIR!!!!
I M RAELLY SORRY, I DINNO U WER A TARGETIIT NOBLE!!!!
PL. FORGIVE ME.......
341@tapan, hey no probs man. BTW, even I did not know I was a "noble". what is that?
@subash - it would be better if you gave me specific examples. Now, pigeonhole principle was something I learnt in JEE coaching. Its a basic principle in combinatorics and is just plain common sense with a title! Do learn it, its uses are varied
21ur profile reads u as targetIIT noble.
sir i also wanted to know y did u say that only one out of +2/-2 can appear on the LHS??
341Thats because the product of those integers is 2. So both 2 and -2 cannot appear on LHS