Question

find the value with complete explanation

Answer 1

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

= ( a + b + c)× 1/2× { 2a² + 2b² +2c² -2ab -2bc -2ca }

= 1/2 (a + b + c){ (a² + b² -2ab )+( b² + c² -2bc) + ( c² +a² -2ac)}

= 1/2( a + b+ c){ (a -b)² + (b -c)² + (c -a)² }

hence,

1/2(a + b + c){(a -b)² + (b -c)² + (c -a)² } = a³ + b³ + c³ -3abc

Answer 2

Answer:

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

= 1/2( a + b+ c){ (a -b)² + (b -c)² + (c -a)² }

hence,

1/2(a + b + c){(a -b)² + (b -c)² + (c -a)² } = a³ + b³ + c³ -3abc