已知X=√2-1,求x3+3x2+4/x2+1的值

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已知X=√2-1,求x3+3x2+4/x2+1的值
已知X=√2-1,求x3+3x2+4/x2+1的值

已知X=√2-1,求x3+3x2+4/x2+1的值
x²=3-2√2=1-2x
x²+2x-1=0
(x^3+3x^2+4)/(x^2+1)
=(x^3+2x^2-x+x^2+x+4)/(x^2+1)
=[x(x^2+2x-1)+x^2+x+4]/(x^2+1)
=(x^2+x+4)/(x^2+1)
=(1-2x+x+4)/(1-2x+1)
=(5-x)(2-2x)
=(6+√2)/(4-2√2)
=7/4 +2√2

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