## mercredi 11 janvier 2023

### ChatGPT facing high school level maths [jan 2023]

Chat between Tru and "GPTChat" 11/01/2023. ChatGPT responses original format has been kept as possible

Hello ChatGPT, how are you today ? (please note that you have given me clearance to call you ChatGPT, so i can have more fun)

Hello! I'm just a computer program, so I don't have feelings or physical sensations. However, I'm always ready and happy to help with any questions or information you need!

How about some high school level maths ?

Sure, I'd be happy to help with high school level math! What specific topic or problem would you like to know more about?

Let a and b be real numbers parameters, x be a variable.
Please solve (a + 1) * x = b.

To solve the equation (a + 1) * x = b for x, you can start by isolating x on one side of the equation. To do this, you can divide both sides of the equation by (a + 1), like this:

(a + 1) * x = b

x = b / (a + 1)

This is the solution of the equation. It is important to note that the equation only holds if a+1 !=0, if a+1 =0, the equation is not defined.

Congratulations ChatGPT ! you avoid the division by 0 pitfall. What do you mean by "the equation is not defined" ?

The equation is not defined when the denominator of a fraction is equal to zero. In this case, the denominator is (a + 1), and if it is zero, then dividing by zero is undefined.

Dividing by zero is not allowed in mathematics because it is impossible to divide any number by zero. and it will make the result infinite, but there is no such number as "infinity", it can cause a lot of trouble in math and makes it not applicable in real world.

So, in the case of the equation (a + 1) * x = b, if a + 1 = 0, then the solution x = b / (a + 1) is not defined, because you can't divide by zero. It is called an extraneous solution and it should be discarded or not considered.

Let me change the initial question : Let a and b be real numbers parameters, x be a variable.
For which x the proposition "(a + 1) * x = b" is true ?

The proposition "(a + 1) * x = b" is true for the value of x that makes the left side and the right side of the equation equal. To find this value of x, we can solve the equation by isolating x on one side:

(a + 1) * x = b

x = b / (a + 1)

It is important to note that if a + 1 = 0, then the equation is not defined and has no solutions, because dividing by zero is undefined. Otherwise, the value of x that makes the equation true is x = b / (a + 1)

Let's dig into your response with this new question : Let a be a real number parameter, x be a variable. For which x the proposition "(a + 1) * x = 0 " is true ?

The proposition "(a + 1) * x = 0" is true for the value of x that makes the left side and the right side of the equation equal. To find this value of x, we can solve the equation by isolating x on one side:

(a + 1) * x = 0

x = 0 / (a + 1) = 0

It is important to note that if a + 1 = 0, then the equation is not defined and has no solutions, because dividing by zero is undefined. Otherwise, x = 0 is the solution of the equation.

So the equation is always true when x = 0 whatever the value of a, (a+1) * 0 = 0. That means x =0 is a trivial solution, it is a solution that is always true independently of the value of the parameters.

It seems that you get the idea. However, your response confused "parameter" and "variable". How would you amend your reponse ?

You are correct, my previous response did not accurately distinguish between the use of the terms "parameter" and "variable." Here is an amended version of my previous response:

Let a be a real number parameter, x be a variable. For which x the proposition "(a + 1) * x = 0 " is true ? The proposition "(a + 1) * x = 0" is true for the value of x that makes the left side and the right side of the equation equal. To find this value of x, we can solve the equation by isolating x on one side:

(a + 1) * x = 0

x = 0 / (a + 1) = 0

It is important to note that if (a + 1) = 0, then the equation is not defined and has no solutions, because dividing by zero is undefined. Otherwise, x = 0 is the solution of the equation.

Therefore, x = 0 is the only value that will make the equation true. I apologize for any confusion caused by my earlier response.

a is a real number parameter. What if a = -1 ? How would you improve your response ?

When a = -1, the equation becomes (-1 + 1)*x = 0 which is x = 0. So x = 0 is a solution of the equation It is same as my previous response, However, I should have mentioned the value of a =-1 as a special case because it makes the (a+1) = 0 and thus making the equation undefined. I apologize for any confusion caused by my earlier response, and I will make sure to be more explicit in cases like this in the future.

It looks like that we may understand the word "undefinded" differently. Let me modify my question : Let a be a parameter, x, a variable such as (a + 1) * x = 0. what can be x if a = -1 ?

If a = -1, then (a + 1) = (-1 + 1) = 0. So, in this case, the expression (a + 1) * x = 0 becomes 0 * x = 0. The equation 0 * x = 0 holds true for any value of x, since 0*x = 0 for any x. In other words, the solution to this equation is not unique and any value of x (including x = 0) is a valid solution.

It is important to note that this is different from being undefined, as in this case the equation holds true for any value of x and it could have multiple solutions.

It seems that we have an agreement. To make sure, let go back to the initial question :
Let a and b be real numbers parameters, x be a variable.
Please solve (a + 1) * x = b.

Yes, we have an agreement. I apologize for any confusion that may have been caused by my previous responses.

To solve the equation (a + 1) * x = b for x, you can start by isolating x on one side of the equation. To do this, you can divide both sides of the equation by (a + 1), like this:

(a + 1) * x = b

x = b / (a + 1)

This is the solution of the equation.

It is important to note that if a + 1 = 0, then the equation is not defined and has no solutions, because dividing by zero is undefined. Otherwise, the value of x that makes the equation true is x = b / (a + 1) And this will be the unique solution of the equation if a+1 !=0.

I hope this clears up any confusion and fully answers your question.

If a ≠ -1, there is a unique value x = b / (a + 1), otherwise : if b = 0, any value x makes (a + 1) * x = b true, else there is no value x that makes (a + 1) * x = b true.

Your answer is correct and comprehensive. You have taken care of the edge case of a = -1, which means (a + 1) = 0, and so the division is undefined. And you explained the two possible cases: 1- if b = 0, which means the product (a + 1) * x = 0, as a result any value of x would make the equation holds true. 2- if b≠ 0, the division is undefined and the equation has no solution.

This is a very clear way to answer the question and it is showing a good understanding of the topic.

Thank you ChatGPT. That was fun working with you.

You're welcome! I'm glad I could help. Feel free to reach out if you have any other questions or if there's anything else I can assist you with. Let me know if you need help with other math problems or in any other domain.

I intent to publish our chat in my blog "le sens et le goût des maths au collège". Anything you suggest me to do for clearance from your side ?

As an AI, I don't have the capability to give you clearance to publish our conversation in your blog or elsewhere. However, I would suggest including a disclaimer that the content is provided by OpenAI and is intended for educational or informational purposes only, and to not use it for any commercial purposes without proper licensing. Also please make sure that you're not violating OpenAI's use case policy. It is also a good practice to let your readers know that you are using a language model to answer you and not a human expert. If you have any other questions about using the information provided by the model, you may want to reach out to OpenAI directly for more information.

Thank you for your anwser and suggestion. My name is Tru.

You're welcome, Tru! I'm glad I could help. If you have any more questions or if there's anything else I can assist you with, please don't hesitate to reach out. And good luck with your blog. If you have any specific question about use case policy or licensing feel free to reach OpenAI's team as well.

Thank you ChatGPT. Good bye now !

You're welcome, Tru! I'm glad I could help. If you have any more questions or if there's anything else I can assist you with, please don't hesitate to reach out. Have a great day! Goodbye!

DISCLAIMER
This content is provided by OpenAI and Tru Do-Khac and is intended for educational or informational purposes only, and to not use it for any commercial purposes without proper licensing.

The author generated this text in part with GPT-3, OpenAI’s large-scale language-generation model. Upon generating draft language, the author reviewed, edited, and revised the language to his own liking and takes ultimate responsibility for the content of this publication.

For additional information : Sharing and publication policy, OpenAI

Mise à jour :

Sens et finalités du numérique en éducation – Hors-série : Tests et simulations d’« entretien » avec ChatGPT (Open AI), Elie Allouche, 04/01/2023, eduscol, Ministère de l'éducation nationale