x*x^(10/x) = (x^x)/(x^2)
Help please..

Question

x*x^(10/x) = (x^x)/(x^2)
Help please..

anonymous · Answer

$$x\left(x^{10/x}\right)=\frac{x^x}{x^2}~~?$$

anonymous · Answer

So i got up to x^2+3x+10=0 
but i don't know what I did wrong.

anonymous · Answer

But this is your equation, right?

anonymous · Answer

yea

anonymous · Answer

$\color{blue}{\text{Originally Posted by}}$ @SithsAndGiggles
$$x\left(x^{10/x}\right)=\frac{x^x}{x^2}~~?$$
$\color{blue}{\text{End of Quote}}$

$$ x^{\frac{10}{x}-1}=x^{x-2}$$
And you thought that because the bases are the same, you have
$$\frac{10}{x}-1=x-2$$
right?

anonymous · Answer

This is as far as I got:

anonymous · Answer

The first problem I'm seeing is that you should have $x^2-3x-10=0$, not plus.

The second is that this doesn't give you all the solutions. I'm not quite sure how to get the remaining ones...

anonymous · Answer

ok thank you.. there's just two more solutions to this

anonymous · Answer

WolframAlpha says $\pm1$ are the remaining solutions, but I'm not sure how one would find these without guessing/checking...

anonymous · Answer

It might involve some logarithms, but that's a wild guess on my part.

anonymous · Answer

well, thank you for your help.. or else I would stuck thinking about what I did wrong.

anonymous · Answer

You're welcome!