Question

If a² + b² + c² − ab − bc − ca =0, then

Options

• a + b + c

•  b + c = a

•  c + a = b

• a = b = c

Answer 1

Given  `a^2 +b^2 +c^2 - ab - bc - ca =0`

Multiplying both sides by 2 we get,

  `2a^2 +2b^2 +2c^2 -ab - 2bc -2ca = 2 xx 0`

`(a^2 - 2ab +b^2 )+ (b^2 -2bc +c^2) + (c^2 -2ac +a^2)= 0`

`(a-b)^2 +(b-c)^2 + (c-a)^2 =0`

Therefore the sum of positive quantities is zero if and only if each quantity is zero.

`(a-b)=0 ,(b-c) = 0,(c-a) =0`

`a=b,b=c.c =a`

If `a^2 +b^2 +c^2 - ab -bc -ca =0`, then  `a=b=c`.