See the new one

-ab should be simplified to the following

i.e

-ab = - (25 + 10√5)^⅓ (25 - 10√5)^⅓

= - (25² - 10² x 5)^⅓

= - (125)^⅓

= -5


But a² and b² still have the exponentials.

i.e a² = (25 + 10√5)^⅔
b² = (25 - 10√5)^⅔


a² + b² will not simplify to (25² + (10√5)²) x 2,

You know how to become perfect square easyvproblrm please go and learn

A + B Perfect square is a square plus b square mijus two ab

We all know that.

The point is, you should be getting

50 = x((a+b)² - 2ab - ab)

50 = x(x² - 2(125)^⅓ - (125)^⅓)

50 = x (x² - 2(5) - 5)

50 = x(x² - 15)

50 = x³ - 15x

x³ - 15x - 50 = 0


Which is not what you wrote above
.

ab = 5, not 125 .

But this method is correct. You should end up with x³ - 15x - 50 = 0 however.

Your idea is is similar to mine (see main comments section)

I used (a + b)³ = a³ + 3a²b + 3ab² + b³

Your method is lengthy and too naggy

You've skipped a lot of steps. That's why

You don’t even know the tricks
The intent of the teacher is to know the property of surfs

I didn’t skip steps

This is how should be done

The thinking processes matter

I suggest if you want to help put in answer not just comments so that we won’t help

Using (a + b)³ = a³ + 3a²b + 3ab² + b³ is equally valid.

The idea is to realise that the middle terms
can be changed into 3(ab)(a+b), which can be easily simplified.

You realised that a³ + b³ = (a + b)(a² - ab + b²) is derived from this, don't you?

Your method in fact, incurred an extra step by having to use a² + b² = (a+b)² - 2ab , which is extra work.

So you used 2 identities :

a³ + b³ = (a + b)(a² - ab + b)²
a² + b² = (a + b)² - 2ab

Compared to my single identity :
(a + b)³ = a³ + 3a²b + 3ab² + b³
= a³ + b³ + 3ab(a+b)

Yet, you say that my method is lengthy and naggy when yours is more complicated but basically uses the same principle of conjugates to reach the same conclusion of x³ - 15x - 50 = 0

My point is, if you want to help, make sure your workings are correct and they lead logically to the next step.

It is my choice whether to post as answer or to write in the comments.

It is far easier to write in comments than to post an answer which would appear as a wall of text.

Handwriting issues are very common here, as we can see from yours (pretty illegible I must say)

Student has to learn
This is Just guide

I am not spoon feeding them because during exam no one can help them

So it remains as a fact that you did skip steps, mainly the expansion of terms and also the evaluation of the conjugates.
(i.e (a + b)^⅓(a - b)⅓ = ((a+b)(a-b))^⅓
= (a² - b²)^⅓

You are free to help or post an alternative answer as a tutor. Perhaps the student likes yours better. If you're so worried about having duplicate answers, then you are free to check the main comments section first.


This is Olympiad Math so knowledge of (a+ b)³ is to be expected, along with a³ + b³ = (a + b) (a² -ab + b²) The latter is only taught in sec 3 for A Math)


a² + b² = (a + b)² - 2ab is also expected as it's already covered in sec 2.

Pls stop writing

If you keep on doing this noone could help the students and not all students are learning at the same methodologies

If you want to write so much I rather you do more math if you are really helpful

I've been in this app long enoug, and have been helping students all the way.

I also try to point out working mistakes that people have, so the students do not risk writing the wrong thing or being misinformed.

Your first picture contained working errors so I was being nice by pointing it out to you.

But now you want to come and call my method too lengthy and naggy, when all I did was to show full working, and it was equally valid.

Whereas yours is brief writings (hardly legible and with mistakes). In fact, this photo here, your second attempt, contained mistakes again (how is the last step 50 = x(x² - 45) ???).

So you have no right to say anything about lengthy and when you have provided inaccurate and incomplete answers in the first place.


You should learn to accept your errors instead of being so defensive. And also, double check your working and proofread before posting.

Saves you embarrassment and keeps your credibility up.

Also, telling someone that he doesn't even know the tricks is just premature judgment and jumping to conclusions.


No one said your method is wrong. I agree with it.

You should also realise that for mathematics, there are multiple approaches to each problem. No one method is superior or inferior to others.

What more, when our answers use the same principle of binomial expansion.

The whole point is to be exposed to different techniques and methods (especially for Olympiad Math)

If you've noticed, many students do not know even where to start or have conceptual gaps. They often ask for elaborate and detailed explanation.

The goal should be to provide working as clear and logical/intuitive as possible.

Guidelines/brief methods only confuse many of them, which would eventually prompt more questions

So, full workings aren't spoon-feeding in this context.