which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0

A:u^2-11u+24=0 where u=(x^2-1)
B:(u^2)^2-11(u^2)+24 where u=(x^2-1)
Cu^2+1-11u+24=0 where u=(x^2-1)
D:(u^2-1)^2-11(u^2-1)+24 where u=(x^2-1)

Question

which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0

A:u^2-11u+24=0 where u=(x^2-1)
B:(u^2)^2-11(u^2)+24 where u=(x^2-1)
Cu^2+1-11u+24=0 where u=(x^2-1)
D:(u^2-1)^2-11(u^2-1)+24 where u=(x^2-1)

thesmartone · Answer

I'll do a similar example for you. Basically, you create a new variable that is equal to something in the quadratic equation so you can simplify it.

$\Large x^6 + 2x^3 + 1 = 0$

$\Large (\color{red}{x^3})^2 + 2(\color{red}{x^3}) + 1 = 0$

Now substitute $\Large \color{red}{u = x^3}$

We use a different variable and not x so we don't get confused. We'll first substitute u in and then solve the equation for u and then solve for x^3 based on what we get for u :)

So substitute u in place of x^3

$\Large (\color{red}{u})^2 + 2(\color{red}{u}) + 1 = 0$

See? Isn't that much easier to solve?

And then you solve for u, and then you set u = x^3 and solve for x since x was what was given to us orginally. But this question is simple and doesn't ask for us to do that much :)

prupel85 · Answer

so its A? or c

thesmartone · Answer

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try from here :)