If x2 + y2 + z2 = 2 (x + z – 1), then the value of : x3

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If x² + y² + z² = 2 (x + z – 1), then the value of :
x³ + y³ + z³ = ?

1. 2
2. 0
3. –1
4. 1

Correct Option: A

x² + y² + z² = 2(x + z – 1)
⇒ x² + y² + z² = 2x + 2z – 2
⇒ x² - 2x + y² + z² - 2z + 2 = 0
⇒ x² - 2x + 1 + y² + z² - 2z + 1 = 0
⇒ (x - 1)² + y² + (z - 1)² = 0
∴ a² + b² + c² = 0 ⇒ a = 0, b = 0, c = 0]
∴ x – 1 = 0 ⇒ x = 1
y = 0
z – 1 = 0 ⇒ z = 1
∴ x³ + y³ + z³ = 1 + 0 + 1 = 2