Question

solve for x, x^4 -2x^2+1=0

Answer 1

can you factor it?

Answer 2

i dont know where to start :(

Answer 3

so it is of the form
\[(a+b)(c+d)=0\]

Answer 4

yer i can do that i think

Answer 5

ok so what will be your a?

Answer 6

x?

Answer 7

have you heard of "completing the square"?

Answer 8

that the worst thing ever but yes

Answer 9

that's what you have to do for this problem so to start:

Answer 10

ok thank you

Answer 11

what number multiplies to 1 but adds to -2?

Answer 12

u tell me

Answer 13

nope tell me

Answer 14

would it be like -1?

Answer 15

please plug it in and tell me if it satisfies the two conditions I gave you

Answer 16

look i got no idea

Answer 17

does -1 multiply to 1

Answer 18

i got it!!!! x=-1 or x=1

Answer 19

close, can you multiply those together and tell me if they =1?

Answer 20

no wouldnt it equal -1?

Answer 21

that is correct. and we know from our original eq. that they need to =1. so what two numbers multiply to positive one?

Answer 22

two negitive = a positive

Answer 23

right, so what multiplies to one?

Answer 24

1

Answer 25

but we wanted negative numbers right?
because then they need to add to -2

Answer 26

yer so the second would be -1?

Answer 27

but they both need to be negative right?

Answer 28

right

Answer 29

so what two negative numbers multiply to 1 and add to -2?

Answer 30

-1

Answer 31

good! now if you know that (a-1)(b-1)=x^4-2x^2+1=0
what are your a and b?

Answer 32

hint: a might equal b

Answer 33

1.factor it first

2.(x^2-1)(x^2-1)=====(x-1)(x+1)(x-1)(x+1)=0

3.x=1or-1??????