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How to solve this equation?

R

RSI

Diamond Member
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
 
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?

 
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
 
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...
 


<< 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
 
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
 


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

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

and from there it's easy 🙂
 


<< 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"
 
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
 


<< 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
 


<<

<< 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
 


<< 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
 


<< 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...
 


<< 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
 
Yep, thanks all. 🙂

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

-RSI
 
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