Inequalities ,my weak sense !

1. The problem statement, all variables and given/known data

hy guys ,help me

prove if x<y and n is odd ,then xn<yn
i have solved this . .but a question in below


2. Relevant equations



3. The attempt at a solution

if 0=or<x<y then xn<yn (i have proved this ) and if x<y<or=0 we can say 0=or<-y<-x it implies -yn<-xn last we can add both side with +xn and +yn we have xn<yn ..
is proved is correct ? and what about if x<y<or=0 ( n is even ) how to prove this ?

thanx before ^_^
 
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last we can add both side with +xn and +yn we have xn<yn
This is correct, or you can also use the fact that multiplying by [tex]-1[/tex] reverses inequalities, i.e., if [tex]A < B[/tex] then [tex]-B < -A[/tex].

is proved is correct ?
You are missing the case where [tex]x < 0 < y[/tex].

and what about if x<y<or=0 ( n is even ) how to prove this ?
In this case, the correct statement is different; try some values for [tex]x[/tex] and [tex]y[/tex], and you should see what it is.
 
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calios said:
and what about if x<y<or=0 ( n is even ) how to prove this ?
You don't need to prove the statement for even n. The statement you're trying to prove explicitly says that n is odd.
 
This is correct, or you can also use the fact that multiplying by [tex]-1[/tex] reverses inequalities, i.e., if [tex]A < B[/tex] then [tex]-B < -A[/tex].



You are missing the case where [tex]x < 0 < y[/tex].



In this case, the correct statement is different; try some values for [tex]x[/tex] and [tex]y[/tex], and you should see what it is.
yes ,thanx for correcting :tongue:
 
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Couldn't you prove these by the process of mathematical induction as well :3 ?
 

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