Johnson

Algebra Level 2

Solve

52, 14 0,6,8 6, 8 0, -6, -8 -6, -8 0

2 solutions

Caleb Townsend
Feb 11, 2015

First, see that $0$ is a solution. So we may divide our equation by $x$ but we must keep in mind that $x = 0$ works as well. $x^3 + 52x = 14x^2 + 4x$ $x^2 + 52 = 14x + 4$ $x^2 - 14x + 48 = 0$ $(x-6)(x-8) = 0$ It is now clear the solutions to this quadratic are $x = 6$ and $x = 8$ , but we must also include the trivial solution of the original problem $x = 0.$ Therefore the solution set is $x \in \{0, 6, 8\}$

Johnson Du
Feb 8, 2015

Moderator note:

This solution is incorrect. The correct answer should be 0, 6, 8.

The solution is a wrong one my friend. How do you know that x is not equal to zero?? How can you suddenly divide it by x without considering the zeroth value of x?? According to my opinion, the solutions should be 0,6,8.

Srutarshi Chakrabarti - 6 years, 4 months ago

Thanks. I have updated the answer to 0, 6, 8.

Calvin Lin Staff - 6 years, 4 months ago

No problem; anytime.

Srutarshi Chakrabarti - 6 years, 4 months ago

@Johnson Du @Stanley Guo With reference to my previous comment, because I am being more aggressive with deleting "bad" problems, I would have deleted this problem because it is not immediately clear to me if the problem creator is intentionally trolling the community.

Note that I edited the question to state that "This problem has no correct option and is undergoing review". I can update the answer to "0,6 , 8", which is what I believe it should be. Otherwise I would be inclined to delete it. Please let me know how you want me to proceed.

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin Hello Calvin, I assigned my students to post problems and solutions on Brilliant for their winter holiday homework. Although I have made every effort to educate them how to correctly do that, there will be unintentional mistakes. I do believe as they practice using Brilliant more and more, they will be better and better at utilizing it and therefore contribute to this community. Is it possible that you can give them some hints or instructions before you finally delete their questions? Cause that will be much more constructive both to the students and to the community. Thank you very much.

Stanley Guo - 6 years, 4 months ago

Hi Stanley,

Thanks for explaining. Now I understand what is happening. We have certainly seen some great problems from your students, like this from David Zhang , this from Harley Guo ,

I initially thought that some mischievous students were abusing the Brilliant platform, which is why I started aggressively deleting. Please let them know that I will be more lenient from now on.

I will resume filing a report indicating what is wrong with their question and what can be improved on. Please ask them to verify their email address, so that they will be informed about these and deal with them accordingly.

I will also maintain this note for your reference, so that you can see the questions that I ahve deleted, along with the reasoning.

Calvin Lin Staff - 6 years, 4 months ago

Sorry, But this solution is wrong . Because at the first step you made after the problem , you have divided both sides by $x$ , and by doing this , unintentionally , you had excluded $0$ from being a correct answer ( because the fraction can not be divided by $0$ ) .

Mohamed Ahmed Abd El-Fattah - 6 years, 4 months ago

You are right. As mentioned below, I have updated the answer to 0, 6, 8.

Let me add a note to this solution.

Calvin Lin Staff - 6 years, 4 months ago

Thank you ^_^ .

Mohamed Ahmed Abd El-Fattah - 6 years, 4 months ago

Johnson

2 solutions

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