解方程:(1)2x^4+3x^3-x^2+2x+3=0 (2)2x^4-7x^3+9x^2-7x+2=0

学习 时间:2026-04-03 09:56:52 阅读:4475
解方程:(1)2x^4+3x^3-x^2+2x+3=0 (2)2x^4-7x^3+9x^2-7x+2=0

最佳回答

害羞的鱼

曾经的铃铛

2026-04-03 09:56:52

(2)可以分解因式:2x^4-7x^3+9x^2-7x+2=(-2 + x) (-1 + 2 x) (1 - x + x^2)。根为:2,1/2,1/2-Sqrt[3]/2,1/2+Sqrt[3]/2。(1)无法像(2)有一个较好的分解,有四次方程的求根公式,但超级复杂,用mathematica、matlab等可以求得(1)有两实根两虚根,很复杂……大约为:-1。82727,-0。8082,0。567737 - 0。832696 i,0。567737 + 0。832696 i。精确值:-(3/8) + 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] - 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) - 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) + 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] + 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) - 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) - 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] - 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) + 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) - 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] + 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) + 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]

最新回答共有2条回答

  • 粗暴的橘子
    回复
    2026-04-03 09:56:52

    (2)可以分解因式:2x^4-7x^3+9x^2-7x+2=(-2 + x) (-1 + 2 x) (1 - x + x^2)。根为:2,1/2,1/2-Sqrt[3]/2,1/2+Sqrt[3]/2。(1)无法像(2)有一个较好的分解,有四次方程的求根公式,但超级复杂,用mathematica、matlab等可以求得(1)有两实根两虚根,很复杂……大约为:-1。82727,-0。8082,0。567737 - 0。832696 i,0。567737 + 0。832696 i。精确值:-(3/8) + 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] - 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) - 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) + 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] + 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) - 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) - 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] - 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) + 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]-(3/8) - 1/2 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)] + 1/2 Sqrt[43/24 - 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) - 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3) + 115/(32 Sqrt[43/48 + 1/6 (1429/2 - (3 Sqrt[152949])/2)^(1/3) + 1/6 (1/2 (1429 + 3 Sqrt[152949]))^(1/3)])]

上一篇 门前的湿漉漉的老是像刚下过一场春雨.这句话是比喻句吗?

下一篇 “亘”的读音