Question

please do this question in your own handwriting useless answer would be reported

Answer 1

4) a²+b²+c²-ab-bc-ca = 0

=> multiply both sides by 2

=> 2(a²+b²+c²-ab-bc-ca) = 2×0

=> 2a²+2b²+2c²-2ab-2bc-2ac = 0

=> a²+a²+b²+b²+c²+c²-2ab-2bc-2ca = 0

=> (a² -2ab+b²)+(b²-2bc+c²)+(c²-2ca+a²) = 0

=> (a-b)²+(b-c)²+(c-a)² = 0

=> sum of positive quantities is zero ,if and only if all quantities are zero .


=> (a-b) = 0 => a = b
=> (b-c) = 0 => b = c
=> (c-a) = 0 => c = a


therefore , a = b = c

hence , proved


hope this helps you