解方程:3x⁴-10x²+3=0
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 20:51:40
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解方程:3x⁴-10x²+3=0
解方程:3x⁴-10x²+3=0
解方程:3x⁴-10x²+3=0
3x⁴-10x²+3=0
(3x²-1)(x²-3)=0
(3x²-1)(x+√3)(x-√3)=0
(√3x-1)(√3x+1)(x+√3)(x-√3)=0
解得 x = ± √3 或 x= ±√3/3
(3x^2-1)(x^2-3)=0
(1) 3x^2-1=0, 3x^2=1,x=±√3/3
(2)x^2-3=0,x^2=3, x=±√3
同学,你好,这道题是换元法的运用
令x^2=t, t≥0
则,原方程=3t^2-10t+3=0
化为 (3t-1)(t-3)=0
t=1/3或3
即 x^2=1/3或x^2=3
所以x=±√3/3或±√3