If x = 997, y = 998 and z = 999 then the value of x² + y² + z² - xy - yz - zx is?

A. 0

B. 1

C. -1

D. 3

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {x^2} + {y^2} + {z^2} - xy - yz - zx \cr & = \frac{1}{2}\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right] \cr} $$
  $$ = \frac{1}{2}$$ $$\left[ {{{\left( {997 - 998} \right)}^2} + {{\left( {998 - 999} \right)}^2} + {{\left( {999 - 997} \right)}^2}} \right]$$
$$\eqalign{ & = \frac{1}{2}\left( {1 + 1 + 4} \right) \cr & = 3 \cr} $$