Question

已知x的2次方+2x-1=0,则x的4次方+2x的3次方-2=

已知x的2次方+2x-1=0,则x的4次方+2x的3次方-2= 详细过程 已知x的2次方+2x-1=0,则x的4次方+2x的3次方+2x-2= 详细过程

Answer 1

x^2+2x-1=0;等式同乘以x^2
==>
x^4+2x^3-x^2=0;
x^4+2x^3-2=x^2-2;
x^2+2x-1=0,==>x^2-2=-1-2x;
接方程x^2+2x-1=0;x=-1+√2;或-1-√2;
x^4+2x^3-2=x^2-2=-1-2x=-1-2(-1+√2)=1-2√2;
或:
x^4+2x^3-2=x^2-2=-1-2x=-1-2(-1-√2)=1+2√2;