If x2 + y2 + 1 = 2x , then the value of x3 + y5 is

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x² + y² + 1 = 2x
⇒ x² + y² + 1 - 2x = 0
⇒ x² - 2x + 1 + y² = 0
⇒ (x – 1)² + y² = 0
⇒ x – 1 = 0
⇒ x = 1 and y = 0
∴ x³ + y⁵ = 1 + 0 = 1