Find all the solutions of x^4 = 1
thanks..
2007-07-10 13:13:23 · 5 answers · asked by rock-onz 1 in Science & Mathematics ➔ Mathematics
1, -1, i, -i
2007-07-10 13:15:57 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
1
2007-07-10 20:21:19 · answer #2 · answered by J.M.C 5 · 0⤊ 1⤋
The answer above is correct. To solve it, I would bring the one to the other side and then factor the polynomial equation.
x^4 - 1 =0 Factor using difference of squares
(x^2 - 1)(x^2 + 1) = 0
(x - 1)(x + 1)(x^2 + 1) = 0
Now set each factor equal to zero.
x- 1=0 gives you x = 1
x + 1=0 gives you x = -1
x^2 + 1 = 0 gives you x^2 = -1 which leads you to the square root of -1 which is i and -i.
So your four answers (if complex answers are allowed) are 1, -1, i and -1. If only real answers are allowed the answers are 1 and -1.
2007-07-10 20:21:22 · answer #3 · answered by keely_66 3 · 1⤊ 0⤋
x=1; x=-1
1^4=1
(-1)^4=1
2007-07-10 20:18:40 · answer #4 · answered by Ainur 2 · 0⤊ 0⤋
I have no clue sry
2007-07-10 20:20:09 · answer #5 · answered by Brittani L 1 · 0⤊ 0⤋