作业帮13-20t+4t*t*t-20t*t*t*t=0,求t?
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 05:21:03
13-20t+4t*t*t-20t*t*t*t=0,求t?
13-20t+4t*t*t-20t*t*t*t=0,求t?
13-20t+4t*t*t-20t*t*t*t=0,求t?
精确解集：
{{t -> 1/20 + 1/20 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) + 10 (487 + 9 Sqrt[9249])^(1/3)] - 1/2 \[Sqrt](1/50 + 8/(487 + 9 Sqrt[9249])^(1/3) - 1/10 (487 + 9 Sqrt[9249])^(1/3) - 999/(50 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) + 10 (487 + 9 Sqrt[9249])^(1/3)]))},
{t -> 1/20 + 1/20 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) + 10 (487 + 9 Sqrt[9249])^(1/3)] + 1/2 \[Sqrt](1/50 + 8/(487 + 9 Sqrt[9249])^(1/3) - 1/10 (487 + 9 Sqrt[9249])^(1/3) - 999/(50 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) +10 (487 + 9 Sqrt[9249])^(1/3)]))},
{t ->1/20 - 1/20 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) +10 (487 + 9 Sqrt[9249])^(1/3)] -1/2 \[Sqrt](1/50 + 8/(487 + 9 Sqrt[9249])^(1/3) -1/10 (487 + 9 Sqrt[9249])^(1/3) + 999/(50 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) +10 (487 + 9 Sqrt[9249])^(1/3)]))},
{t ->1/20 - 1/20 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) +10 (487 + 9 Sqrt[9249])^(1/3)] +1/2 \[Sqrt](1/50 + 8/(487 + 9 Sqrt[9249])^(1/3) -1/10 (487 + 9 Sqrt[9249])^(1/3) + 999/(50 Sqrt[1 - 800/(487 + 9 Sqrt[9249])^(1/3) +10 (487 + 9 Sqrt[9249])^(1/3)]))}}
数值解集
{{t -> -1.10388},{t -> 0.363254- 0.942286 i},{t -> 0.363254+ 0.942286 i},{t -> 0.577369}}
解析解是个很复杂的根式，还是告诉你数值解吧，t1＝-1.10388，t2＝0.577369，t3＝0.363254 - 0.942286 I,t4＝0.363254 - 0.942286 I，其中I是虚数单位。