Question

a,b,c are distinct real numbers such that a³ = 3 (b²+c²) –25, b³ = 3(c²+a²) –25, c³ = 3 (a² + b²) – 25. Find the numerical value of abc.

Answer 1

a³ – b³ = 3(b² – a²) => a² + b² + ab = – 3 (a + b)     ....(i)