Question

How do you find the x-intercepts of x^(4)-8x^(2)+8?

Answer 1

\[x^4-8x^2+8=0\]

Why don't you try substitution of \[u = x^2\] to turn it into a quadratic:
\[u^2-8u+8=0\]Solve that by your favorite method, then undo the substitution.

Answer 2

I got it, thank you!

Answer 3

What did you get for your answers?

Answer 4

\[x=-\sqrt{4-\sqrt{2}}, \sqrt{{4}-\sqrt{2}}, -\sqrt{{4}+\sqrt{2}},\sqrt{{4}+\sqrt{2}}\]

Answer 5

Oops, not so fast...those aren't quite correct.

Answer 6

What did I do wrong?

Answer 7

Should be a 2 in front of all of the \(\sqrt{2}\)'s there

Answer 8

\[x = \pm\sqrt{4\pm2\sqrt{2}}\]

Answer 9

Oh yeah, I just forgot to write in the 2 before the square root of 2. I have it in my work though.

Answer 10

Ah, okay. We'll let you keep that medal ;-)

I was worried that you might think there were only 2 solutions, so when I saw you had 4, I gave you the medal before I checked them closely :-)

Answer 11

Thank you for your help!

Answer 12

you're welcome!