已知α,β是方程X²+2X-5=0的两个实数根α²+β²+3α+3β的值为多少?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 22:03:17
![已知α,β是方程X²+2X-5=0的两个实数根α²+β²+3α+3β的值为多少?](/uploads/image/z/1592718-6-8.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%2C%CE%B2%E6%98%AF%E6%96%B9%E7%A8%8BX%26%23178%3B%2B2X-5%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%CE%B1%26%23178%3B%2B%CE%B2%26%23178%3B%2B3%CE%B1%2B3%CE%B2%E7%9A%84%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91%3F)
已知α,β是方程X²+2X-5=0的两个实数根α²+β²+3α+3β的值为多少?
已知α,β是方程X²+2X-5=0的两个实数根α²+β²+3α+3β的值为多少?
已知α,β是方程X²+2X-5=0的两个实数根α²+β²+3α+3β的值为多少?
α,β是方程X²+2X-5=0的两个实数根,则
α+β=-2 αβ=-5
α²+β²+3α+3β
=(α+β)²-2αβ+3(α+β)
=(-2)²-2(-5)+3(-2)
=4+10-6
=8
α+β=-2
αβ=-5
α²+β²+3α+3β
=(α+β)²-2αβ+3(α+β)
=4+10-6
=8
X²+2X-5=0
(x+1)²=6
x=-1±根号6
α²+β²+3α+3β
=(-1+根号6)²+(-1-根号6)²+3(-1+根号6)+3(-1-根号6)
=8