solutions of -x^3+3x^2-3x+1
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We know that:
(a - b)^3 = a^3 - 3*a^2*b + 3*a*b^2 - b^3
Rearranging the above:
(-b + a)^3 = -b^3 + 3*a*b^2 - 3*a^2*b + a^3
-b^3 + 3*a*b^2 - 3*a^2*b + a^3 = (-b + a)^3
So -x^3 + 3x^2 - 3x + 1 = 0 can be written as
(-x + 1)^3 = 0
=> (1 - x)^3 = 0
(1 - x)(1 - x)(1 - x) = 0
1 - x = 0, 1 - x = 0, 1 - x = 0
x = 1, 1, 1 ——> Answer
(a - b)^3 = a^3 - 3*a^2*b + 3*a*b^2 - b^3
Rearranging the above:
(-b + a)^3 = -b^3 + 3*a*b^2 - 3*a^2*b + a^3
-b^3 + 3*a*b^2 - 3*a^2*b + a^3 = (-b + a)^3
So -x^3 + 3x^2 - 3x + 1 = 0 can be written as
(-x + 1)^3 = 0
=> (1 - x)^3 = 0
(1 - x)(1 - x)(1 - x) = 0
1 - x = 0, 1 - x = 0, 1 - x = 0
x = 1, 1, 1 ——> Answer
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