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Verified answer
X² + y² = 2x + y = 1
(x + y)² = 1²
x² + y² + 2xy = 1
2 + 2xy = 1
2xy = 1 - 2
xy = -1/2
(x² + y²) = 2²
x⁴ + y⁴ + 2x²y² = 4
x⁴ + y⁴ + 2(-1/2)² = 4
x⁴ + y⁴ + 1/2 = 4
x⁴ + y⁴ = 4 - 1/2
x⁴ + y⁴ = 3 1/2