已知a²-3a+1=0.求a+1/a、a²+1/a²和(a-1/a)²的值

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已知a²-3a+1=0.求a+1/a、a²+1/a²和(a-1/a)²的值

已知a²-3a+1=0.求a+1/a、a²+1/a²和(a-1/a)²的值
已知a²-3a+1=0.求a+1/a、a²+1/a²和(a-1/a)²的值

已知a²-3a+1=0.求a+1/a、a²+1/a²和(a-1/a)²的值
a²-3a+1=0
等式两边同除以a
a-3+1/a=0
a+1/a=3
a²+1/a²
=(a+1/a)²-2
=3²-2
=9-2
=7
(a-1/a)²
=(a+1/a)²-4
=3²-4
=9-4
=5


a^2-3a+1=0,所以:a-3+1/a=0,所以:a+1/a=3
a^2+1/a^2=(a+1/a)^2-2=9-2=7
(a-1/a)^2=(a+1/a)^2-4=9-4=5

方程两边除以a 则a+1/a等于3 平方得a²+1/a²等于7 则(a-1/a)²等于5