数学方程3x²+11x+3<0请解
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/25 21:49:18
数学方程3x²+11x+3<0请解
![数学方程3x²+11x+3<0请解](/uploads/image/z/4437963-27-3.jpg?t=%E6%95%B0%E5%AD%A6%E6%96%B9%E7%A8%8B3x%26%23178%3B%2B11x%2B3%EF%BC%9C0%E8%AF%B7%E8%A7%A3)
解不等式3x²+11x+3<0
3x²+11x+3=3[x²+11x/3]+3=3[(x+11/6)²-121/36]+3=3(x+11/6)²-121/12+3
=3(x+11/6)²-85/12=3[(x+11/6)²-85/36]
=3[(x+11/6)+(√85)/6][(x+11/6)-(√85)/6]
=3[x+(11+√85)/6][x+(11-√85)/6]
3x²+11x+3=3[x²+11x/3]+3=3[(x+11/6)²-121/36]+3=3(x+11/6)²-121/12+3
=3(x+11/6)²-85/12=3[(x+11/6)²-85/36]
=3[(x+11/6)+(√85)/6][(x+11/6)-(√85)/6]
=3[x+(11+√85)/6][x+(11-√85)/6]