Question

solve by substituting a variable to simplify the equation: x^4+2x^2=8
How do i get the answer; + or - the square root of 2 and + or - 2i

Answer 1

Try substituting y=x^2. So your equation is now:

y^2+2y=8

Answer 2

okay then y^2+2y-8=0?

Answer 3

Yup! You're on the right track!

Answer 4

okay but where did the "i" come from in the answer?

Answer 5

Well, when you factor you get:
(y+4)(y-2)=0

So y=-4 or y=2
which means
x^2=-4 or x^2=2
square root both sides and you get
x=+-2i and x=+-sqrt2

Answer 6

thanks!