Consider three real numbers \(a\), \(b\), \(c\) with \(abc = 1\). Prove that the equation

\[ax^4 + (2b + a)x^2 - 2cx + b^3c + bc + bc^3 = 0\]

has no real roots!

Doti reāli skaitļi \(a\), \(b\) un \(c\), kuriem \(abc = 1\). Pierādīt, ka vienādojumam

\[ax^4 + (2b + a)x^2 - 2cx + b^3c + bc + bc^3 = 0\]

nav reālu sakņu!