How could I solve this system of equations with 3 variables, and others with more variables?

Question

6=a+b+c

11=a*b+(a+b)*c

6=abc

And other ones with more variables such as

10=a+b+c+d

35=a*b+(a+b)*c+(a+b+c)*d

50=(abc)+d((a*b)(a+b)*c)

24=abcd

So that I can get the roots of higher degree polynomials without having to approximate.

Thanks.

Answer 1

Roots of $$ x^3 - 6 x^2 + 11x-6, $$ $$ x^4 - 10x^3 + 35 x^2 - 50 x + 24. $$ Which seem to be $(1,2,3)$ and $(1,2,3,4)$

SEE VIETE