I’ve been working on this question related to reducible quadratic equations and have ended up with 4 solutions i.e. x=1, x=1, x=-1, x=-1
now, I am aware that general rule of sets does not allow repetition of numbers within the set. So, how do I construct the solution set for my question based on these results?
for further refrence, following is the reduced form of the equation I was dealing with.
x^4 - 2x^2 + 1 = 0
this is how I went about solving it:
(x^2)^2 - 2(x^2)(1) + (1^2) = 0 i.e. a^2 + 2(a)(b) + (b^2) = 0
(x^2 - 1)^2 = 0
(x^2-1)(x^2-1) = 0
(x+1)(x-1)(x+1)(x-1) = 0 i.e. a^2 - b^2 = (a+b)(a-b)
therefore, x=1, x=1, x=-1, x=-1
how to construct the solution set now?
now, I am aware that general rule of sets does not allow repetition of numbers within the set. So, how do I construct the solution set for my question based on these results?
for further refrence, following is the reduced form of the equation I was dealing with.
x^4 - 2x^2 + 1 = 0
this is how I went about solving it:
(x^2)^2 - 2(x^2)(1) + (1^2) = 0 i.e. a^2 + 2(a)(b) + (b^2) = 0
(x^2 - 1)^2 = 0
(x^2-1)(x^2-1) = 0
(x+1)(x-1)(x+1)(x-1) = 0 i.e. a^2 - b^2 = (a+b)(a-b)
therefore, x=1, x=1, x=-1, x=-1
how to construct the solution set now?