Seriously, why is the answer so important?

So I think that many people has seen this. So why do some people still have such a thought, that whenever a problem is seen, always try "All (some) of the variables are equal."? (Of course, guessing is acceptable, but typing out the solution that way is awkward!!!)

Just curious, so don't blame me please. And yup, I did do so, but only for guessing.

#Algebra

Easy Math Editor

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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Annie Li - 3 years, 11 months ago

I just want to let the numbers grow. Anyways, you are not the first one who asks me this XD

Steven Jim - 3 years, 11 months ago

People have different interpretations of what constitutes a "solution". Not everyone is trained in rigor / proofs.

In such a scenario, I love to link to inequalities with strange equality conditions.

Calvin Lin Staff - 3 years, 11 months ago

Excuse me, I don't really get it. Can you please explain further?

About the link, I did mention it in my note.

Steven Jim - 3 years, 11 months ago

People have different interpretations of what constitutes a "solution". They think that "Oh, because I tried these variables and got the numerical answer, hence I am correct". They are not aware of what a proof is, and why they need to (in this case) rigorously demonstrate that they have found an extrema, instead of just "I happened to enter the correct answer".

It is quite a common misconception that expressions achieve their extrema when all variables are equal. This is not true even if we restrict our attention to cyclic or even symmetric expressions. To further drive home this point, I link out to the wiki which has a lot of such examples.

Calvin Lin Staff - 3 years, 11 months ago

@Calvin Lin – Thanks for the lesson.

Steven Jim - 3 years, 11 months ago

What is the problem called?

Annie Li - 3 years, 11 months ago

"BAM k is max" it is.

Steven Jim - 3 years, 11 months ago

It's easier to just give the link here.

To answer your question, most people are not really interested in figuring out how to solve it, the education system has brought them up that way.

Pi Han Goh - 3 years, 11 months ago

@Pi Han Goh – Yeah. Thanks for the link. I'll try to remember the LaTeX next time :)

To be honest, I'm very surprised. I've already heard of such education system (at least in my city) but typing the answers ONLY is not why Brilliant is made (I think). Besides, I don't think that an American (nope, I don't want to imply anything, seriously) will give such a solution. I mean their education system, in my opinion, is very improved. That raises me to this question.

Also, if only it was 2 or 3, that'd be great. But I think I've seen about 50 solutions (sorry, I mostly do Inequalities so I don't know much about other topics) with stuff like "Answer is... when..." and no clear explanation. If I could remember them, I'd have posted it here so you could see how awkward it is.

Anyways, can you please explain more about such system? I think I haven't known everything about that (all I know is that teachers fake their scores so they could promote, and students now just try to solve problems without understanding what they are doing).

Steven Jim - 3 years, 11 months ago

@Steven Jim – It's not just in inequalities problems only. If you look at those "Basic" problems in the "Problems of the week", most of the solutions there are not properly written, because the author most likely can't clearly express why the answer is correct. Moreover, most users don't have the proper motivation to properly learn these stuffs, because in their entire life, they were told that "you only get marks if you follow my arbitrary steps of instructions." Heck, you are actually encouraged to blindly remember formulas without having the slightest clue on what you have learned in the entire semester.

Pi Han Goh - 3 years, 11 months ago

@Pi Han Goh – Well... That's not what I expected, you know. Thanks anyways.

Steven Jim - 3 years, 11 months ago

What is the link for brilliant lounge? Is it accessible through the brilliant website?

Annie Li - 3 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$