What is the proof for xn<yn when x<y and n is odd?

In summary, the conversation is about proving the statement "if x<y and n is odd, then xn<yn". The person asking for help has solved the proof for the case where x < 0 < y and is wondering if it is correct. They are also asking for help in proving the statement for the case where x<y<0 and n is even. The other person suggests using the fact that multiplying by -1 reverses inequalities and reminds them to also consider the case where x < 0 < y. They also mention that the statement may be different for the case where n is even and suggest trying out some values to see what it is. The conversation ends with a question about using mathematical induction to prove the statement.
  • #1
calios
9
0

Homework Statement



hy guys ,help me

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


Homework Equations





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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  • #2
calios said:
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].

calios said:
is proved is correct ?

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

calios said:
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.
 
  • #3
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.
 
  • #4
ystael said:
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:
 
  • #5
Couldn't you prove these by the process of mathematical induction as well :3 ?
 

What are inequalities?

Inequalities are mathematical expressions that compare two quantities and show which one is greater than, less than, or equal to the other.

What is the difference between an inequality and an equation?

An inequality compares two quantities and shows their relationship, while an equation states that two quantities are equal.

What is the purpose of studying inequalities?

Studying inequalities allows us to analyze and understand real-world situations, make predictions, and solve problems.

How do you solve an inequality?

To solve an inequality, first isolate the variable on one side of the inequality sign and then use inverse operations to simplify and solve for the variable.

What is the importance of understanding "my weak sense" in inequalities?

Understanding your weak sense in inequalities allows you to identify and address any difficulties or misconceptions you may have in solving inequalities. This can help improve your overall understanding and ability to solve more complex problems.

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