题目内容

若x=
3
+1
,则y=2x5-4x4-x3-6x2-6的值为______.
由x=
3
+1
得3=(x-1)2
∴y=2x5-4x4-x3-6x2-6
=2x3(x2-2x+1)-2x3-x3-6x2-6
=2x3(x-1)2-3x3-6x2-6
=2x3×3-3x3-6x2-6
=3x3-6x2-6
=3x(x2-2x)-6
=3x(x2-2x+1)-3x-6
=3x(x-1)2-3x-6
=3x•3-3x-6
=9x-3x-6
=6x-6
=6(x-1)
=6
3
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