因为α、β是方程x²-x-1=0的两个根所以α² - α - 1 = 0所以α² = α + 1根据韦达定理有 α + β = 1 α^4+3β = （ α + 1）² + 3β = α² + 2 α + 1 + 3β = 3α + 2 + 3β = 3(α +β ...