Inequality equation help

  • Thread starter penguin007
  • Start date
  • #1
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Hi everyone,

Homework Statement



P(X)=Xp-1*(X-1)p*...*(X-n)p

j is an integer between 1 and n;
x a real beatween 0 and 1.

Prove that abs(P(jx))<=(n!)p

Homework Equations





The Attempt at a Solution



I tried to find an inequality for each abs(jx-q) but the problem is that I can't control j*x...


Any clue is welcome!
 

Answers and Replies

  • #2
35,017
6,767


Hi everyone,

Homework Statement



P(X)=Xp-1*(X-1)p*...*(X-n)p

j is an integer between 1 and n;
x a real beatween 0 and 1.

Prove that abs(P(jx))<=(n!)p

Homework Equations





The Attempt at a Solution



I tried to find an inequality for each abs(jx-q) but the problem is that I can't control j*x...


Any clue is welcome!

Please show us what you've tried. In particular, what do you have for P(jx)?
 
  • #3
77
0


Please show us what you've tried. In particular, what do you have for P(jx)?

For p(jx), you mean?:
P(jx)=(jx)p-1*(jx-1)p...(jx-n)p

I wanted to find an inequality for each abs((jx-q)), but my problem is that since jx is between 0 and n, I don't know the sign of jx-q...

I also tried:
* abs(jx-q)<=q, but this inequality is obviously wrong(for q=5, x=1 and j=11)...

*abs(P(jx))<=abs(P(j)) or abs(P(jx))<=abs(P(n*x)) so I could get rid of x or of j,but here too, these inequalities appears to be wrong...
 
Last edited:

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