Question

a²+ab+ca divided by b²-(c+a)​

Answer 1

Answer:

Now,

a²+b²+c²-ab-bc-ca

= ½ • ( 2a²+2b²+2c²-2ab-2bc -2ca )

= ½ • ( a² -2ab +b² +b² -2bc +c² +c² -2ac +a² )

= ½ • { (a-b)² + (b-c)² + (c-a)² }

For any value of a,b,c

(a-b)² ≥ 0,

(b-c)² ≥ 0,

(c-a)² ≥ 0,

So,

a²+b²+c²-ab-bc-ca = ½ • { (a-b)² + (b-c)² + (c-a)² } ≥ 0 i.e. Non-negative [ proved ]