已知X=2倍的根号2+1,求分式X^2-2X-9/X^2-11X-15的值

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已知X=2√2+1,求分式(X^2-2X-9)/(X^2-11X-15)的值.
由已知X=2√2+1移项,得
X-1=2√2
两边平方,得
X^2-2X+1=8
X^2=2X+7
把上式代入下式的分子和分母,得
(X^2-2X-9)/(X^2-11X-15)
=(2X+7-2X-9)/(2X+7-11X-15)
=-2/(-9X-8)
=2/(9X+8)
=2/[9(2√2+1)+8]
=2/[18√2+17]
=2(18√2-17)/[(18√2+17)(18√2-17)]····注：分母有理化；
=2(18√2-17)/(648-289)
=2(18√2-17)/359

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