解一元四次方程X^4+4X^3+2X^2-5X=2
问题描述:
解一元四次方程X^4+4X^3+2X^2-5X=2
答
x^4+4x^3+2x^2-5x-2=0x^4-x^3+5x^3-5x^2+7x^2-7x+2x-2=0x^3(x-1)+5x^2(x-1)+7x(x-1)+2(x-1)=0(x-1)(x^3+5x^2+7x+2)=0(x-1)(x^3+2x^2+3x^2+6x+x+2)=0(x-1)[x^2(x+2)+3x(x+2)+(x+2)]=0(x-1)(x+2)(x^2+3x+1)=0x=1,x=-2,...