已知x+1/x=4,①求x²+1/x² ②求（x-1/x)²的值

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已知x+1/x=4,①求x²+1/x²②求（x-1/x)²的值已知x+1/x=4,①求x²+1/x²②求（x-1/x)²的值已知x+1/x=

已知x+1/x=4,①求x²+1/x² ②求（x-1/x)²的值
已知x+1/x=4,①求x²+1/x² ②求（x-1/x)²的值

x+1/x=4
①两边平方
x²+2×x×1/x+1/x²=16
x²+1/x²=16-2
x²+1/x²=14
②∵x²+1/x²=14
x²-2×x×1/x+1/x²=14-2
∴(x-1/x)²=12