Question

已知X=√2-1,求x3+3x2+4/x2+1的值

Answer 1

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