Diberikan y+x = 1 dan x²+y² = 2. Berapakah nilai x^4 + y^4?

x² + y² = 2
x + 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