已知x - 1/x = 3/2,则分式x² + 1/x²的值

已知x - 1/x = 3/2,则分式x² + 1/x²的值
已知x - 1/x = 3/2,则分式x² + 1/x²的值

已知x - 1/x = 3/2,则分式x² + 1/x²的值
x - 1/x = 3/2 平方
x² -2+ 1/x²=9/4
x² + 1/x²=17/4

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x - 1/x = 3/2, 2x²-2=3x , (2x+1)(x-2)=0, x=-1/2 , x=2
x² + 1/x²=1/4+4=4.25