1. ## formula question

hi! is this correct???

2. Hi

No, it's wrong, unless * is the symbol you use for the sum and + the one you use for the product...

3. Hello,

Not it isn't.

$\displaystyle a^{{\color{red}n}*k}$ (I suppose it's n, not a) is equal to $\displaystyle (a^n)^k=(a^k)^n$

The only thing you can do is to factor by $\displaystyle a^k$, if $\displaystyle k<n$ :

$\displaystyle a^n+a^k=a^k \left(a^{n-k}+1 \right)$

4. Originally Posted by yuriythebest
hi! is this correct???

no.....the only manipulation I could see would be this $\displaystyle a^n+a^k=a^n(1+a^{k-m})$

and to test your hypothesis let a=2 and k=1 and n=2

5. wow thanks for the lighting-quick responses. But it seems I am still doing something terribly wrong:

6. I'd make a substitution :

$\displaystyle u=(x^3+8)^{1/4}$

Then the equation is now u²+u=6

7. ok I tried it that way but it seems I am going around in circles...

8. No, you're not "going around in circles". Once you have found the two solutions $\displaystyle u_1,\,u_2$ of $\displaystyle u^2+u-6=0$, you can solve for $\displaystyle x$ : $\displaystyle \sqrt[4]{x^3+8}=u_1 \Rightarrow x^3+8=u_1^4$ and so on...

Be careful about $\displaystyle \Delta=b^2-4ac=1^2-4\times 1\times (-6)\neq 40$

9. ok I tried that and got 2 negative roots:

10. OK you got the idea, now, read again the post #8. (especially the last sentence "Be careful...")

11. thank you flyingsquirrel! answer iz correct!

12. Originally Posted by yuriythebest
thank you flyingsquirrel! answer iz correct!
I'm referring to post #7: I don't understand where you've got the results from:

$\displaystyle u^2+u-6=0~\implies~u = -3~\vee~u=2$

And therefore

$\displaystyle \sqrt[4]{x^3+8} = -3$ that means there doesn't exist a real x to satisfy this equation

or

$\displaystyle \sqrt[4]{x^3+8} = 2~\implies~x^3+8=16~\implies~x^3=8~\implies~\boxed {x=2}$

13. yeah I understood that. cause of my spelling I mistook one of my u's for a 4 and therefore the incorrect answer. With your help I redid it and everything is correct.