Need some help with this problem!

[SiberianOwner]

Ok, so I have been trying to figure out this problem for like, I think 2 days now.... :shock:

Solve the Equation By Factoring

x^4 - 10x^2 + 9= 0
This is what I got so far...

x(x^3 -10x)+9=0
I factored down the 10, and added all the factors together, and got (-1 and 10) to equal 9.

Now, I'm stuck and don't know what do do next? Do I factor out the 9 as well?

The problem is asking for 4 answers so far I got
x=?
X=?
x=1(correct)
x=?-----from smallest to largest.

Grrr, I'm so ready to give up on this one LOL. :evil:

 

[pka]

\(\displaystyle x^4 - 10x^2 + 9 = \left( {x^2 - 1} \right)\left( {x^2 - 9} \right)\)

 

[Deleted member 4993]

Ok, so I have been trying to figure out this problem for like, I think 2 days now.... :shock:

Solve the Equation By Factoring

x^4 - 10x^2 + 9= 0
This is what I got so far...

x(x^3 -10x)+9=0
I factored down the 10, and added all the factors together, and got (-1 and 10) to equal 9.

Now, I'm stuck and don't know what do do next? Do I factor out the 9 as well?

The problem is asking for 4 answers so far I got
x=?
X=?
x=1(correct)
x=?-----from smallest to largest.

Grrr, I'm so ready to give up on this one LOL. :evil:

Substitute

u = x[sup:n0y9j2bm]2[/sup:n0y9j2bm]...................................(1)

then you r turns into

u[sup:n0y9j2bm]2[/sup:n0y9j2bm] - 10 u + 9 = 0.......................(2)

(2) is a quadratic equation - solve it for 'u', by your favorite method.

Then solve for 'x' using (1).

 

[SiberianOwner]

Ok that actually cleared up how I was supposed to get four answers out of that because thats what was confusing me the most. I think my biggest problem is I dont know where to put numbers when it comes to factoring.

Did you factor it down again to get to u^2? and where is the u from, i'm so confused with this problem lol

 

[pka]

Did you factor it down again to get to u^2? and where is the u from, i'm so confused with this problem lol

I am one who hates the u-substitutes.
Look how easy it really is.
\(\displaystyle x^4 - 10x^2 + 9 = \left( {x^2 - 1} \right)\left( {x^2 - 9} \right)\).
Just learn to factor. That is very simple binominal.

 

[SiberianOwner]

Wow that is alot easier than I was making it, I looked at that a few times, and tried it on a different problem and now I understand how to factor. But I don't know how to get 4 answers out of that. Out of everything I covered in Class this week, this is the only thing My brain can not seem to understand...

 

[Denis]

If a^2 = 25, then a = 5 or -5 ; -5 * -5 = 25 :wink: Now kick yourself :!: