m2-5m-1=0,求2m2-5m+1/m2的值

m2-5m-1=0,求2m2-5m+1/m2的值
m2-5m-1=0,求2m2-5m+1/m2的值

m2-5m-1=0,求2m2-5m+1/m2的值
∵m²-5m - 1 = 0
∴5m = m² - 1 -------------------①
m1 + m2 = 5
m1xm2 = -1
∴m1² + m2² = 27
设2m²-5m+1/m² = x -----------------------②
由①②得
(m²)² + (1-x)m² + 1 = 0
（m1）² + m2² = x - 1
∴x = 28