How to solve this equation?

[RSI]

x^4 - 25x² + 144 = 0

How to get the solution(s) to this equation? If you transpose the 144 to the other side it becomes -144, in which case you can't find the square root of a negative number. You can factor X^4 and -25x², but that just gives you x²(x²-25).. how does that help? We still need the 144. Or can we just leave it as x²(x²-25) + 144 = 0 ? I don't think you can... but I don't know. I'm confused and my head is pounding right now.

Any help for a math bobo... appreciate it..

-RSI

 

[Novgrod]

Crap; I know I can solve this 'un.

why not take the square root of each side?

x^2 - 5x + 12 = 0

Erm; I haven't done this in so long . . .

I can't figure that it factors, but does this help?

 

[RSI]

No, I considered that too.

But how are you supposed to get the square root of a negative number? It's not possible. Any square equates to a positive number. Therefore you can't find the root of a negative number, because no square could equal a negative number. Get it?

Still stumped...

-RSI

 

[Stealth1024]

you can't do that the way you want to: afterall the squate root of 4 + 4 is not 2 + 2

 

[worth]

x^4 - 25x² + 144 = 0
x^4 - 25x² = -144
-(25x^2-x^4) = -144
25x^2-x^4 = 144
(5x-x^2)^2=144
5x-x^2=12

quadratic that shiznit or maybe factor, and you're done...

 

[Sciolist]

Ever hear of a little thing called the quadratic formula?

Check it out here: quadratic formula

(Using this, you can solve for X squared, then solve for X)

(So you have X = 4 and X = 3)

 

[CStroman]

Use the quadratic formula on x^2-5x+12+0.

 

[Novgrod]

edit: i feel stupid. haven't looked at a math book in three years

 

[rgwalt]

<< x^4 - 25x² + 144 = 0
x^4 - 25x² = -144
-(25x^2-x^4) = -144
25x^2-x^4 = 144
(5x-x^2)^2=144
5x-x^2=12

quadratic that shiznit or maybe factor, and you're done... >>



Your second to last step here is incorrect.

Let me think about this one... I used to know how to do these... nowadays I would just solve it numerically (w/ a calculator).

Ryan

 

[RSI]

I know about the quadratic formula. You can't get the square root of a negative number which is what you end up with using the quadratic formula.

Could it be that this question does not work?

-RSI

 

[worth]

<< Your second to last step here is incorrect. >>



And why is not? Not saying that I'm not wrong, I'm kind of tired too

 

[Novgrod]

okay; think i figured it out the easy way: factors to;

(x^2 - 9) (x^2 - 16) = 0

and from there it's easy

 

[Platypus]

<< I know about the quadratic formula. You can't get the square root of a negative number which is what you end up with using the quadratic formula.

Could it be that this question does not work?

-RSI >>



Ever hear of imaginary numbers?

Ie: "i"

 

[rgwalt]

Yeah, let y=x^2, then you get

y^2 - 25y +144 = 0

Use the quadratic formula (if you've learned that in math already) to find two roots of y. (y1 and y2)

x1 = +sqrt(y1) or -sqrt(y1)
x2 = +sqrt(y2) or -sqrt(y2)

You have to test all four roots.

Ryan

 

[Sciolist]

It's still easier the way I did it above; use the quadratic to solve for X squared.

 

[RSI]

<< okay; think i figured it out the easy way: factors to;

(x^2 - 9) (x^2 - 16) = 0

and from there it's easy >>

:Q I think you got it... :Q:Q gimme a sec...

-RSI

 

[worth]

I still don't get what's wrong with my solution

 

[rgwalt]

<<

<< Your second to last step here is incorrect. >>



And why is not? Not saying that I'm not wrong, I'm kind of tired too >>





<< 25x^2-x^4 = 144
(5x-x^2)^2=144 >>



This is because x^4 + y^4 =/ (x^2 + y^2)^2, which is what you imply.

Ryan

 

[RSI]

<< I still don't get what's wrong with my solution >>

It doesn't matter. We're all morons. x²-9 and x²-16. Two differences of squares, factoring to (x-3)(x+3) and (x-4)(x+4). why the hell didn't I see that damn simple factor?

-RSI

 

[bigalt]

wow that thread was painful to read

 

[rgwalt]

The quadratic formula works too.

Ryan

 

[worth]

<< This is because x^4 + y^4 =/ (x^2 + y^2)^2, which is what you imply. >>



Doh, I knew something was wrong

I confused x^2 - y^2 = (x-y)(x+y)... I knew I was tired...

 

[RSI]

<< The quadratic formula works too.

Ryan >>

It didn't seem to when I tried to use the quadratic formula I would get a negative number under the root..

-RSI

 

[rgwalt]

I tried the quad. form. and didn't have a problem.

eh, oh well, problem solved.

Ryan

 

[RSI]

Yep, thanks all.

I'll probably get stuck on the next question.. nah, I should be good to go now. Thanks again.

-RSI