SOLUTION: x^4-3x^2-10=0 solve by making the appropriate substitution.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: x^4-3x^2-10=0 solve by making the appropriate substitution.      Log On


   

Question 4386: x^4-3x^2-10=0 solve by making the appropriate substitution.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-+3x%5E2+-+10+=+0
Let u+=+x%5E2, which means that u%5E2+=+x%5E4

Substitute these into the original equation to obtain:
u%5E2+-+3u+-+10+=+0, which can be factored into
%28u-5%29%28u%2B2%29=0

Solve for u, and get
u+=+5 or u=-2

Next substitute back into u+=+x%5E2
u+=+5 or u=-2
x%5E2+=+5 or x%5E2+=+-2

Are you solving for real solutions or do you need all real or complex solutions? Either way, take square root of each side of both equations.

First equation:
x%5E2+=+5
x+=+sqrt+%285%29 or x+=+-sqrt+%285%29

Second equation:
x%5E2+=+-2
x+=+sqrt+%28-2%29 or x+=+-sqrt+%28-2%29
x+=+i+%2A+sqrt+%282%29 or x+=+-+i%2Asqrt+%282%29

R^2 at SCC