16 设x=--------,求x^5+2x^4-17x^3-x^2+18x-17的值 √17+1
问题描述：
16 设x=--------,求x^5+2x^4-17x^3-x^2+18x-17的值 √17+1
16
x=--------
√17+1
答
x=16/(√17+1)=16(√17-1)/(√17+1)(√17-1)=16(√17-1)/(17-1)=√17-1
所以x^5+2x^4-17x^3-x^2+18x-17
=x^5+2x^4+x^3-18x^3-x^2+18x-17
=x^3*(x^2+2x+1)-18x^3-x^2+18x-17
=x^3*(x+1)^2-18x^3-x^2+18x-17
=x^3*(√17-1+1)^2-18x^3-x^2+18x-17
=-x^3-x^2+18x-17
=-x^3-2x^2-x+x^2+19x-17
=-x(x^2+2x+1)+x^2+19x-17
=-x*(√17-1+1)^2+x^2+19x-17
=-17x+x^2+19x-17
=x^2+2x-17
=(x+1)^2-18
=(√17-1+1)^2-18
=17-18
=-1
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