+37 Let a, b, c be complex numbers, with a real, such that
a+b+c = ab + ac + bc = abc = 3.
Find a.
I see that b = d + ei and c = d - ei, for some real d and e.
I used vietas and got a system of three equations in a, d and e, which idk how to solve :(
+289 Use polynomial construction!
S_1 = 3
S_2 = 3
S_3 = 3
We can then construct a polyoimial where a, b, c are roots of this polynomial.
P(x) = x^3 - 3x^2 + 3x - 3
= (x - 1)^3 - 2
(x-1)^3 = 2
Since I believe a has to be real based on the fact that b = d + ei and c = d - ei , \(a = \sqrt[3]{2} + 1\)
+289 Use polynomial construction!
S_1 = 3
S_2 = 3
S_3 = 3
We can then construct a polyoimial where a, b, c are roots of this polynomial.
P(x) = x^3 - 3x^2 + 3x - 3
= (x - 1)^3 - 2
(x-1)^3 = 2
Since I believe a has to be real based on the fact that b = d + ei and c = d - ei , \(a = \sqrt[3]{2} + 1\)
