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
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