== 那个,貌似好像是我打的式子出了点问题
4x/(x²+x+3) + 5x/(x²-5x+3)= - 3/2
请见谅,能不能重新解释下题目?
4x/(x²+x+3)+ 5x/(x²-5x+3)= - 3/2
x{4/(x²+x+3)+ 5/[(x²+x+3)-6x]}= - 3/2
令x²+x+3=y,则原式化为:
x[4/y+5/(y-6x)]=-3/2 等式两边同乘以2y(y-6x)
2x[4(y-6x)+5y]=-3y(y-6x)
2x(9y-24x)=-3y(y-6x)
18xy-48x²=18xy-3y²
48x²-3y²=0
(4x)²-y²=0
(4x+y)(4x-y)=0
4x+y=0或4x-y=0
将x²+x+3=y代入4x+y=0得:
4x+x²+x+3=0
x²+5x+3=0
x²+2*(5/2)x+(5/2)²+3-25/4=0
(x+5/2)²=13/2²
x=√13/2-5/2=(√13-5)/2或x=-√13/2-5/2=(-√13-5)/2
将x²+x+3=y代入4x-y=0得:
4x-x²-x-3=0
x²-3x+3=0
x²-2*(3/2)x+(3/2)²-9/4+3=0
(x-3/2)²=3/2²
x=3/2±√3/2=(3±√3)/2