If x = b + c - 2a, y = c + a - 2b, z = a + b - 2c, then the value of x² + y² - z² + 2xy is?

A. 0

B. a + b + c

C. a - b + c

D. a + b - c

Answer: Option A

Solution(By Examveda Team)

x = b + c - 2a
y = c + a - 2b
z = a + b - 2c
⇒ x + y + z = (b + c - 2a) + (c + a - 2b) + (a + b - 2c) = 0
∴ Now,
⇒ x² + y² + 2xy - z²
⇒ (x + y)² - z² [∴ (a² - b²) = (a + b) (a - b)]
⇒ (x + y - z) (x + y + z)
As we know, (x + y + z) = 0
∴ x² + y² - z² + 2xy
= 0 × (x + y - z)
= 0