3

Part of 2020 South Africa National Olympiad

Problems(1)

SAMO Problem 3: Solution to system of polynomial equations

Source: South African Mathematics Olympiad 2020, Problem 3

x

y

z

are real numbers satisfying \begin{align*} (x + 1)(y + 1)(z + 1) & = 3 \\ (x + 2)(y + 2)(z + 2) & = -2 \\ (x + 3)(y + 3)(z + 3) & = -1, \end{align*} find the value of

(x + 20)(y + 20)(z + 20).

algebrapolynomialsystem of equations