x^4+x^3+1的因式分解
因式分解：x^4+x^3+1 一个学生问的题目，好几个老师一起想，都没有一个好方法来分解，哪位高手帮忙一下！
全部回答
好像没法分解。
>> factor(x^4+x^3+1) ans = x^4+x^3+1 >> solve('x^4+x^3+1','x') ans = -1/4+1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+1/12*(-(-18*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+6*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)+288*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+18*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4+1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-1/12*(-(-18*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+6*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)+288*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+18*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4-1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+1/12*6^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)-48*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+3*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4-1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-1/12*6^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)-48*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+3*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) 。
>> factor(x^4+x^3+1) ans = x^4+x^3+1 >> solve('x^4+x^3+1','x') ans = -1/4+1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+1/12*(-(-18*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+6*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)+288*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+18*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4+1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-1/12*(-(-18*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+6*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)+288*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+18*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4-1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+1/12*6^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)-48*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+3*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) -1/4-1/12*3^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-1/12*6^(1/2)*((3*(108+12*i*687^(1/2))^(1/3)*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)-((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)*(108+12*i*687^(1/2))^(2/3)-48*((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2)+3*3^(1/2)*(108+12*i*687^(1/2))^(1/3))/(108+12*i*687^(1/2))^(1/3)/((3*(108+12*i*687^(1/2))^(1/3)+2*(108+12*i*687^(1/2))^(2/3)+96)/(108+12*i*687^(1/2))^(1/3))^(1/2))^(1/2) 。
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