Question

u substitution
x^4-8x^2-9 = 0
u = x^2
u²-8u-9 = 0
can this be factored or do I need the quadratic?

Answer 1

Two numbers that multiply to -9 and add to -8: -9 and 1


So replace -8u with -9u+1u to get

u²-8u-9 = 0

u²-9u+1u-9 = 0

u(u-9)+1(u-9)=0

(u+1)(u-9)=0

u+1=0 or u-9=0

u=-1 or u=9

Since u = x^2, we know that

x^2=-1 or x^2=9

So x = i, x=-i, x=3, or x=-3

Answer 2

holy pellet I can't believe I didn't see that lmao. thanks jim. I must be tired.

Answer 3

u²-8u-9 = 0
u²-9u+u-9 = 0
(u-9)(u+1)=0
u=9,u=-1
u=x^2
x^2=9, x^2=-1
x=3
x=-3 ,

Answer 4

lol the solution is imaginary so that may explain why you didn't see it

Answer 5

no i didn't see 9-1 = 8 lol.

Answer 6

i was like, derp 3 x 3 does not = 8 when I add them.. fudge..