Substance 0
New member
- Joined
- May 8, 2020
- Messages
- 6
I need seriously need help with this one Let p, q∈R. Prove that if 1/p^2−p is irrational, then p is irrational. A similar example would also help a lot thx
Which one is your problem:I need seriously need help with this one Let p, q∈R. Prove that if 1/p^2−p is irrational, then p is irrational. A similar example would also help a lot thx
I am relatively sure that it is \(\dfrac{1}{p^2-p}\). And that is \(\dfrac{1}{p-1}-\dfrac{1}{p}\).I need seriously need help with this one Let p, q∈R. Prove that if 1/p^2−p is irrational, then p is irrational.
I would try to prove the contrapositive. Can you state that? Can you then prove it?I need seriously need help with this one Let p, q∈R. Prove that if 1/(p^2−p) is irrational, then p is irrational. A similar example would also help a lot thx
Would that prove that p is irrational?I am relatively sure that it is \(\dfrac{1}{p^2-p}\). And that is \(\dfrac{1}{p-1}-\dfrac{1}{p}\).
If \(a=\dfrac{3}{11}\) \(a\) rational and \(\dfrac{1}{a}=\dfrac{11}{3}\) which is rational also.
What \(a-1\)~? Rational? Thus if we suppose that \(p\) is rational does that lead to a contradiction?
I don't know how toIf a/b is irrational will b/a be irrational?? Yes, this is true. can you state why??
So then p(p-1) is irrational. How can you conclude that p is irrational.
For the record, Dr Peterson suggestion to use the contrapositive will make this problem simple.
Please look at the contrapositive. Can you state it? In not, then please tell us and we will show you how to get the contrapositive.
I suggested using the contrapositive largely because I guessed that your problem would be in the context of a course in which you would have been taught such things (or will soon).I don't know how to
If p is not irrational then 1/p^2-p is not irrationalThe contrapositive of If A then B is If not B then not A.
Those two statement are logically the same. They are basically the same statement. So proving one is the same as proving the other.
Now can you state the contrapositive of if 1/p^2−p is irrational, then p is irrational?
You need to use parentheses!
.
.
.
I noticed that. That is what I get for pasting what the OP wrote--after scolding them about it not being right. Ouch.Jomo, even after you made an edit to your post #10, you were guilty of
(supposedly unintentionally) leaving off the grouping symbols in the
denominator that you scolded the original poster, which your post in
this quote box refers to.