1. ## Equivalent Forms

$\displaystyle ^3\sqrt{2} (\sqrt{3)$ is equal to?

an equivalent form of $\displaystyle (2\sqrt{2} - \sqrt{6})^2$ is ?

(This is also an excuse for me to get used to the php math code, which I never used before)

2. Originally Posted by zoso
$\displaystyle ^3\sqrt{2} (\sqrt{3)$ is equal to?

an equivalent form of $\displaystyle (2\sqrt{2} - \sqrt{6})^2$ is ?

(This is also an excuse for me to get used to the php math code, which I never used before)
I see no way to simplify the first expression. Note: A slightly better way to code the cube root of 2 is: $\displaystyle \sqrt[3]{2}$ (Click to see the code.)

$\displaystyle \left ( 2 \sqrt{2} - \sqrt{6} \right ) ^2 = \left ( 2 \sqrt{2} \right ) ^2 - 2 \cdot \left ( 2 \sqrt{2} \right ) \left ( \sqrt{6} \right ) + \left ( - \sqrt{6} \right ) ^2$

$\displaystyle = 4 \cdot 2 - 2 \cdot 2 \sqrt{12} + 6 = 14 - 4 \sqrt{12}$

$\displaystyle = 14 - 4 \cdot 2 \sqrt{3} = 14 - 8 \sqrt{3}$

-Dan

3. Originally Posted by zoso
$\displaystyle ^3\sqrt{2} (\sqrt{3)$ is equal to?

an equivalent form of $\displaystyle (2\sqrt{2} - \sqrt{6})^2$ is ?

(This is also an excuse for me to get used to the php math code, which I never used before)
$\displaystyle \sqrt[3]{2}\sqrt{3}=\sqrt[6]{4}\sqrt[6]{27}=\sqrt[6]{108}$

Malay

4. Originally Posted by zoso
(This is also an excuse for me to get used to the php math code, which I never used before)
Here's a tutorial if you haven't seen it yet.

5. k, I'm going to go read the tutorial, then come back and try something else out.

6. ok, lets try posting with fractions

Simplfy $\displaystyle \frac {1} {x + 1} - \frac {3} {x - 1}$ assuming $\displaystyle x \neq\pm 1$

$\displaystyle \frac {1} {j + 20} - \frac {1} {j} = 400$

$\displaystyle \frac {1} {j} - \frac {1} {j + 20} = 1$

$\displaystyle \frac {400} {j + 20} - \frac {400} {j} = 1$

$\displaystyle \frac {400} {j} - \frac {400} {j + 20} = 1$

M drives 400 in one hour less than J. If M's speed is 20 km/h faster than J's, what is the proper equation to determine the speed of J?

7. Originally Posted by zoso
ok, lets try posting with fractions

Simplfy $\displaystyle \frac {1} {x + 1} - \frac {3} {x - 1}$ assuming $\displaystyle x = \pm 1$ (What is the tag for non-equivalents? that should read "assuming, x is not equal to..")
$\displaystyle x \neq \pm 1$
or
$\displaystyle x \not =\pm 1$

something interesting:

$\displaystyle \frac{8}{4}\quad\Rightarrow\quad\frac{\not2\times \not2\times 2}{\not2\times \not2}\quad\Rightarrow\quad2$

8. Originally Posted by zoso
ok, lets try posting with fractions

Simplfy $\displaystyle \frac {1} {x + 1} - \frac {3} {x - 1}$ assuming $\displaystyle x \neq\pm 1$

$\displaystyle \frac {1} {j + 20} - \frac {1} {j} = 400$

$\displaystyle \frac {1} {j} - \frac {1} {j + 20} = 1$

$\displaystyle \frac {400} {j + 20} - \frac {400} {j} = 1$

$\displaystyle \frac {400} {j} - \frac {400} {j + 20} = 1$

M drives 400 in one hour less than J. If M's speed is 20 km/h faster than J's, what is the proper equation to determine the speed of J?
Anyone going to work through these two, quickly?

9. Originally Posted by zoso
ok, lets try posting with fractions

Simplfy $\displaystyle \frac {1} {x + 1} - \frac {3} {x - 1}$ assuming $\displaystyle x \neq\pm 1$
find the common denominator...
$\displaystyle \frac {1(x-1)} {(x + 1)(x-1)} - \frac {3(x+1)} {(x - 1)(x+1)}$

multiply: $\displaystyle \frac {x-1} {x^2 + 1} - \frac {3x+3} {x^2 + 1}$

subtract: $\displaystyle \frac {x-1-3x-3} {x^2 + 1}$

group like terms: $\displaystyle \frac {x-3x-1-3} {x^2 + 1}$

subtract: $\displaystyle \frac {\neg 2x-4} {x^2 + 1}$

10. So, $\displaystyle \frac {-2(x + 2)} {x^2 - 1}$ ?

11. Originally Posted by zoso
So, $\displaystyle \frac {-2(x + 2)} {x^2 - 1}$ ?
yes, I'm glad you realized that, it should be written as, $\displaystyle \neg2\frac {x + 2} {x^2 + 1}$ though

12. Originally Posted by Quick
yes, I'm glad you realized that, it should be written as, $\displaystyle \neg2\frac {x + 2} {x^2 + 1}$ though
$\displaystyle -2 \frac {x + 2} {x^2 + 1} = - \frac {2(x + 2)} {x^2 + 1} = \frac {-2(x + 2)} {x^2 + 1}$

I don't see why any one form should be more "correct" than any other. As far as I know there is no consensus on any particular form.

Also, Quick: Why do you keep using "$\displaystyle \neg$" as opposed to simply "-"?

-Dan

13. Originally Posted by topsquark
$\displaystyle -2 \frac {x + 2} {x^2 + 1} = - \frac {2(x + 2)} {x^2 + 1} = \frac {-2(x + 2)} {x^2 + 1}$

I don't see why any one form should be more "correct" than any other. As far as I know there is no consensus on any particular form.

Also, Quick: Why do you keep using "$\displaystyle \neg$" as opposed to simply "-"?

-Dan
I think they are looking for simplest form...

BTW: I am starting to use the $\displaystyle \neg$ for negative numbers, particularly fractions.

14. Originally Posted by Quick
I think they are looking for simplest form...

BTW: I am starting to use the $\displaystyle \neg$ for negative numbers, particularly fractions.
But why use it? As far as I know, "-" is standard for at least complex numbers.

-Dan