Question

. If a² + b² + c² = ab + bc + ca, then the value
of a³ + b³ + c³ is​

Answer 1

Answer:

3abc

Step-by-step explanation:

Using identity a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-(ab+bc+ca))

But ab+bc+ca = a²+b²+c²

=> a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-(a²+b²+c²))

=> a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-a²-b²-c²)

=> a³+b³+c³-3abc = (a+b+c) × 0

=> a³+b³+c³-3abc = 0

=> a³+b³+c³ = 3abc