1.已知a²-3a+1=0,求a²+(a^-2)的值
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![1.已知a²-3a+1=0,求a²+(a^-2)的值](/uploads/image/z/12072920-32-0.jpg?t=1.%E5%B7%B2%E7%9F%A5a%26%23178%3B-3a%2B1%3D0%2C%E6%B1%82a%26%23178%3B%2B%EF%BC%88a%5E-2%EF%BC%89%E7%9A%84%E5%80%BC)
1.已知a²-3a+1=0,求a²+(a^-2)的值
1.已知a²-3a+1=0,求a²+(a^-2)的值
1.已知a²-3a+1=0,求a²+(a^-2)的值
a²-3a+1=0
除以a得
a-3+1/a=0
a+1/a=3
(a+1/a)²=3²
a²+1/a²+2=9
a²+1/a²=7
a²+a^-²=7
解,把a²-3a+1=0除以a,得a-3+1/a=0,则可以得出,a+1/a=3,
而a²+(a^-2)其实=(a+1/a)的平方-2,则=9-2=7