# Thread: Joined forum just to settle a query?

1. ## Joined forum just to settle a query?

Hi

I was helping a student with her H/w and she had taken some screenshots of the whiteboard of her teachers explanation/answer.

When I looked at it, I thought hmmm... not sure you can do that...?

I'd like some answers before divulge what it was and what I believe it to be.. It's drove me nuts for days thinking have I got this wrong. Don't want to misguide her.

Quite simply this is the question.

1. 4y=x^2 ......Make "x" the subject of..?

Thanks for looking.

2. ## Re: Joined forum just to settle a query?

Originally Posted by JCoutts
not sure you can do that...?
I'd like some answers before divulge what it was and what I believe it to be.. It's drove me nuts for days thinking have I got this wrong. Don't want to misguide her.
Quite simply this is the question.
1. 4y=x^2 ......Make "x" the subject of..?
Assuming that what is meant by subject is $x$ is a function of$y$[I] the the answer would be, $x=2\sqrt{y}$.
Discussion: because $x^2\ge 0,~\forall x$ it implies that $y\ge 0$.

3. ## Re: Joined forum just to settle a query?

Hmm.. that is what the teacher showed, but what i don't understand is how the 4y term has been split with the root.? As you have also shown..?

1. 4y=X²
2. Then root to both sides…
3. So.. √X² = ±√4y…. simplifying…..gives
4. Ans. X = ±2y.

What have I done incorrectly. Please explain.?

Thanks

4. ## Re: Joined forum just to settle a query?

Originally Posted by JCoutts
Hmm.. that is what the teacher showed, but what i don't understand is how the 4y term has been split with the root.? As you have also shown..?
1. 4y=X²
2. Then root to both sides…
3. So.. √X² = ±√4y…. simplifying…..gives
4. Ans. X = ±2y.
Your's is a common mistake. The square root of two is written as $\sqrt2$
If one writes $\pm\sqrt2$, that is two different numbers. One of which is the positive root, $\sqrt2$, the other is the negative root, $-\sqrt2$.

The notation $\pm\sqrt2$ is really just short-hand notation. Because of the so-called vertical line rule for functions, to say $y=x^2$ the for every $x$ there is only one corresponding $y$.

5. ## Re: Joined forum just to settle a query?

O.K - I thought the ± was because the √X² could be a positive or a negative number we don't know what x is? or y for that matter. e.g Parabolic function.

So one more thing in your method why is only the Y rooted in your answer, is 2√y, so by this you have split the original term 4y or 2y. Shouldn't the route go over the whole term?

Or as with your above answer is that to keep the 2 a positive integer.? Maybe you could write your method out as I have.(Steps).

Thanks

6. ## Re: Joined forum just to settle a query?

Originally Posted by JCoutts
O.K - I thought the ± was because the √X² could be a positive or a negative number we don't know what x is? or y for that matter.
That is another very common misstake.
$\Large\sqrt{X^2}\ne \pm X$.
In fact, $\Large\sqrt{X^2}\ne X$.

The correct answer is, $\Large\sqrt{X^2}= |X|$

If you are tutoring, I suggest you learn the facts.

7. ## Re: Joined forum just to settle a query?

Well, I am 46yrs old and so it's a looonnng time since I was at school/college/university granted. I apologise for not getting it.

I have no problem in admitting when I am wrong, but I do like to understand what happened.

I can quite understand a root & square cancel, as that part I got to correctly. As for learning the rules I thought when you swap & applied the inverse you do it to both sides wholly, so it is the "Y" side 4y that I have not understood what it got to.

How it went from 4y to 2√y, why it wasn't across the whole term. Forget about the X side for the moment Y oh why oh why is the root between the number and the variable.?

8. ## Re: Joined forum just to settle a query?

Originally Posted by JCoutts
I can quite understand a root & square cancel, as that part I got to correctly. As for learning the rules I thought when you swap & applied the inverse you do it to both sides wholly, so it is the "Y" side 4y that I have not understood what it got to.

How it went from 4y to 2√y, why it wasn't across the whole term. Forget about the X side for the moment Y oh why oh why is the root between the number and the variable.?
Frankly, I do not understand your concerns.
If you had $4y-x^2=0$ and told to make $x$ a subject(function) of $y$.
\begin{align*}x^2&=4y\\x^2&=4y\\x&=\sqrt{4y}\\&=2 \sqrt{y} \\ \end{align*}

9. ## Re: Joined forum just to settle a query?

O.K - In my quest to get an understanding I came across this site which I duly plugged the equation in.

It is the rule (circled) that I did not apply correctly, and the penny has finally dropped...

What I do notice is they have put the ± in the answer too.

Thank you so much for being patient with me.. got there in the end. I shall try and remember that.