MathDB

Suppose that

\omega, a,b,c

are distinct real numbers for which there exist real numbers

x,y,z

that satisfy the following equations: x\plus{}y\plus{}z\equal{}1, a^2 x\plus{}b^2 y \plus{}c^2 z\equal{}\omega ^2, a^3 x\plus{}b^3 y \plus{}c^3 z\equal{}\omega ^3, a^4 x\plus{}b^4 y \plus{}c^4 z\equal{}\omega ^4. Express

\omega

in terms of

a,b,c

Problem Statement