You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Loki123
- Start date

- Joined
- Mar 16, 2016

- Messages
- 3,128

2 + sqrt(5) > 4, so if you If you sub 2 + sqrt(5) into the RHS, the RHS will be negative.

- Joined
- Dec 30, 2014

- Messages
- 11,455

In this problem, I would simply solve the problem and then check my answer to see if any are erroneous.

Also stop using a calculator to see what 2+ sqrt(5) lies between.

We know that 2=sqrt(4) < sqrt(5) < sqrt(9) = 3. So sqrt(5) lies between 2 and 3. Hence 4 = 2+2 < 2 + sqrt(5) < 2+3 = 5. So yes, sqrt(5)>4!

What is RHS?

2 + sqrt(5) > 4, so if you If you sub 2 + sqrt(5) into the RHS, the RHS will be negative.

We were taught to find the domain which is why I am trying to do it that way. I tried to just check the answers, but they both ended up working. Here is my work on that:

In this problem, I would simply solve the problem and then check my answer to see if any are erroneous.

Also stop using a calculator to see what 2+ sqrt(5) lies between.

We know that 2=sqrt(4) < sqrt(5) < sqrt(9) = 3. So sqrt(5) lies between 2 and 3. Hence 4 = 2+2 < 2 + sqrt(5) < 2+3 = 5. So yes, sqrt(5)>4!

I know I should have rationalized them and, therefore, eliminated the square roots from the denominator, but I pretty sure that doesn't change anything. I probably went somewhere wrong, however, I checked it multiple times and couldn't find out where.

- Joined
- Jun 18, 2007

- Messages
- 25,839

- Joined
- Apr 22, 2015

- Messages
- 3,800

[math]\sqrt{1 - \dfrac{4}{4 - x}} = \dfrac{4}{4 - x}.[/math]

Obviously, if 4 - x is a denominator, then x cannot equal 4. Moreover, if x is greater than 4, then the right hand side of the equation is negative, but a square root is necessarily non-negative. Therefore, x must be less than 4.

[math]\sqrt{1 - \dfrac{4}{4 - x}} = \dfrac{4}{4 - x} \implies 1 - \dfrac{4}{4 - x} = \dfrac{16}{(4 - x)^2} \implies (4 - x)^2 - 4(4 - x) = 16 \implies \\ 16 - 8x + x^2 - 16 + 4x = 16 \implies x^2 - 4x - 16 = 0 \implies x = \dfrac{4 \pm \sqrt{(-4)^2 - 4(1)(-16)}}{2 * 1} \implies \\ x= \dfrac{4 \pm {16 + 64}}{2} = \dfrac{4 \pm {80}}{2} = \dfrac{4 \pm 2\sqrt {5}}{2} = 2 \pm \sqrt{5}.[/math]

This is what you got. But you

However, we previously determined that x < 4. And obviously

[math]4 < 5 \implies 2 \le \sqrt{5} \implies 2 + \sqrt{5} > 4 \implies x \ne 2 + \sqrt{5}.[/math]

Therefore that answer is not relevant based on the domain restriction. Our brilliant resident feline explained that way back in post 2.

- Joined
- Dec 30, 2014

- Messages
- 11,455

RHS means right hand side.What is RHS?

- Joined
- Dec 30, 2014

- Messages
- 11,455

For example if you have

Also, since you are are checking to see if the left hand side equals the right hand you should NOT use equal signs! Equals signs are used when you know that what is on side of the equal sign equals what is on the other side of the equal sign. The reason that you squared bot sides is because you felt that both sides are equal. You should put a question mark over the equal sign.

Maybe he thought this was “Different Equations”?

- Joined
- Aug 27, 2012

- Messages
- 1,286

Please understand that I'm no longer getting on your case but is your class actually named "Mathematics?" What is the exact name of the class?

-Dan

Mathematics. But we call it just math.Please understand that I'm no longer getting on your case but is your class actually named "Mathematics?" What is the exact name of the class?

-Dan

To be honest, I don't like how the education system is where I am, I think multiple classes on different subjects relating to mathematics would have been better, but I can't really do anything about it other than learn.

- Joined
- Jan 27, 2012

- Messages
- 7,770

arithmetic

algebra

geometry

trigonometry

pre-calculus

calculus

advanced algebra

differential equations

differential geometry

and more.

We were hoping for a more specific label than just "mathematics" so we could better see exactly what it is you are trying to do.

I was trying to see if it's true by simplifying it... I got the same result on both side at the end, where did I make a mistake for that to happen if the equation is not true?Not quite, Loki. In your check below, that first equation is not true (as the cat had noted, in post #2).

View attachment 29054

It says that 4.2361 equals -4.2361 (rounded).

- Joined
- Apr 22, 2015

- Messages
- 3,800

You'd started the check with a false equation. See post #7. That equation is not true.where did I make a mistake

Perhaps I am not explaining myself the best. Imagine if the = wasn't there. I didn't move anything from one side to the other so it makes no difference. So say I was just repeating same actions on two problems, how did I in the end get them to equal the same thing if they weren't the same from the start?You'd started the check with a false equation. See post #7. That equation is not true.

- Joined
- Mar 16, 2016

- Messages
- 3,128

-2 = 2 (which is clearly not true).

If you square both sides, you get

4 = 4 (which is true).

That is effectively what you have done!