How to solve this index question?

[Ocean]

Would you be able to help with this question?
Simplify [z^(4)+ z^(-4) - 3] / [z^(2) + z^(-2) - 5^(1/2)]

The answer is z^(2) + z^(-2) + 5^(1/2) but I can’t seem to get to it.

 

[tkhunny]

Have you considered factoring?

 

[Denis]

Simplify [z^(4)+ z^(-4) - 3] / [z^(2) + z^(-2) - 5^(1/2)]

The answer is z^(2) + z^(-2) + 5^(1/2) but I can’t seem to get to it.

start with:
let x = 5^(1/2) ; it'll be a little less confusing...

 

[Steven G]

z^(4)+ z^(-4) - 3 = (z^(4)+ z^(-4) + 2) - 5 =(z^(4)+ z^(-4) + 2) - (5^1/2)²
Factor the first set of parenthesis (the bold ones). Then use one of your special formulas to factor the whole numerator.

 

[Steven G]

start with:
let x = 5^(1/2) ; it'll be a little less confusing...

Denis, seriously I do not agree with your substitution making things easier. Look at my post above.

 

[Denis]

Denis, seriously I do not agree with your substitution making things easier. Look at my post above.

Yer missing my point:
I'd rather "write down" x than 5^(1/2) as I'm solving;
saves time; substitute back in at end.

Tip for Ocean:
a^n + a^(-n) = a^n + 1/a^n = [a^(2n) + 1]/a^n

 

[Steven G]

Yer missing my point:
I'd rather "write down" x than 5^(1/2) as I'm solving;
saves time; substitute back in at end.

Tip for Ocean:
a^n + a^(-n) = a^n + 1/a^n = [a^(2n) + 1]/a^n

Try doing it with your sub using my method and see how nicely it comes out