x^4 - 5x^2 = 36
2006-12-10 07:13:02 · 3 answers · asked by deano899 1 in Science & Mathematics ➔ Mathematics
(x^2+4)(x^2-9)
2006-12-10 07:16:04 · answer #1 · answered by Peeps 3 · 0⤊ 0⤋
Your first step would be to bring everything over to the left hand side.
x^4 - 5x^2 - 36 = 0
This can actually be solved *like* a quadratic, in that x^4 splits up into x^2 and x^2. This is how we approach the problem; we factor it just like that. In fact, this does factor into:
(x^2 - 9 ) (x^2 + 4) = 0
Yielding
x^2 - 9 = 0
x^2 + 4 = 0
We throw away the second equation for this reason:
x^2 + 4 = 0
x^2 = -4, but there are no real solutions because the square of a number is always positive. This leaves us with only x^2 - 9 = 0 to solve.
x^2 - 9 = 0
Factor as a difference of squares
(x - 3) (x + 3) = 0
Giving the result x = 3 and x = -3.
2006-12-10 07:17:02 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
Let u = x^2.
u^2 - 5u - 36 = 0
(u - 9)(u + 4) = 0
u = x^2 = 9 [the only choice, since x^2 can't be -4].
x = 3 or -3.
2006-12-10 07:42:14 · answer #3 · answered by S. B. 6 · 0⤊ 0⤋