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](/uploads/image/z/18661123-19-3.jpg?t=%E5%B7%B2%E7%9F%A5X%3D%E2%88%9A2-1%2C%E6%B1%82x3%2B3x2%2B4%2Fx2%2B1%E7%9A%84%E5%80%BC)
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
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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