Eyes on Final Fantasy Forums > Reference > Study Hall > Maths help...

[Selena_Akariko]

x² + x + x^-1 + x^-2 = 4

I have been trying to solve this for more than 3 hours now, but I have no idea how to do it I've tried lots of different ways, but none of them worked.

So... Help? Please?

Selena
>>

[Kirobaito]

x = 1

lol

As for how to solve it, I have no idea... but the answer is x = 1.

[Flying Mullet]

That's a doozy. I rewrote the problem as:
x² + x + 1/x + 1/x² = 4
then converted everything to a common denominator of x² which gave me this:
(x⁴ + x³ + x + 1) / x² = 4
but that's as far as I got.

I'm sure there's some identity or such that can be applied here, I just can't think of any that fit the bill.

EDIT:
You can then factor the numerator into:
(x³ + 1)(x + 1)
which you can cut into:
(x³ + 1)/x * (x + 1)/x = 4

[rubah]

i'd graph it imo

-2.618024
-.381966
+1.00 (.99999999965 yeah I dunno about that either!)

Note that there is a hole in the graph at x=0 since you have to divide by x, lol not happenin'!

also there's a good chance I might have graphed it wrong, and a definite chance that there's some fractional representation of those decimals

[Selena_Akariko]

Kirobaito: Wish it was that easy... Our teacher requires the solving, not the result

Flying Mullet,

(x³ + 1)(x + 1)
which you can cut into:
(x³ + 1)/x * (x + 1)/x = 4

Well, I tried that, but it doesn't seem to give any hints about how to solve it...

This problem is supposed to turn out very easy once you find the way how to do it... At least, that's how other problems in that textbook worked.

rubah, I'm afraid graphing isn't an option

Selena

Edit: The answer is supposed to be: x1 = x2 = 1; x3,4 =(-3 ± √5)/2

[rubah]

well, the thing about graphing is that once you have your answers, you can then start to work backwards sometimes, and then you'll realize how to do it. that's how I did a lot of trig homework xD

Anyways, -2.61etc *2 +3 +sqrt5 happens to be 0 so I'm pleased that that answer was correct
-.381etc * 2 +3 -sqrt5 is also zero 8)

sorry i can't help you do it algebraicly

[Flying Mullet]

Originally Posted by Selena_Akariko ^

Kirobaito: Wish it was that easy... Our teacher requires the solving, not the result

Flying Mullet,

(x³ + 1)(x + 1)
which you can cut into:
(x³ + 1)/x * (x + 1)/x = 4

Well, I tried that, but it doesn't seem to give any hints about how to solve it...

This problem is supposed to turn out very easy once you find the way how to do it... At least, that's how other problems in that textbook worked.

rubah, I'm afraid graphing isn't an option

Selena

Edit: The answer is supposed to be: x1 = x2 = 1; x3,4 =(-3 ± √5)/2

I didn't figure out how to solve it. I was hoping that it might help out in some way.

[blackmage_nuke]

This might sound like a noob method but i moved the 4 to the left side to get
x^2+x+1/x+1/x^2-4=0
then i did the same thing as flying mullet and made one denominator
(x4 + x3 + x + 1 - 4)/x2 = 0

So i just ignored that bottom x2 because i can move it to the other side
Then i tested values for x4+x3+x+1-4 until it = 0 to find a factor
1 was a factor
(x-1)(x3+2x2-2x-1)=0
Then i subed for x3+2x2-2x-1 until i found a factor
1 was a factor
(x-1)(x-1)(x2+3x+1)
from here u get x=1 or x2+3x+1=0 which u can use the quadratic formula for x = (-3+root5)/2

Ive never been good at remembering or applying any of the larger theorems or rule so this might not be the quickest way