1

Part of 2020 Nigerian Senior MO Round 2

Problems(1)

Viete and polynomials

Source: Nigeria Olympiad senior mathematics round 2 2020 no 1

k

be a real number. Define on the set of reals the operation

x*y

\frac{xy}{x+y+k}

x+y

-k

x_1<x_2<x_3<x_4

be the roots of

t^4=27(t^2+t+1)

[(x_1*x_2)*x_3]*x_4=1

. Find all possible values of

k

Algebra Polynomialsalgebrapolynomial