2.解方程:x2+3x-根号(x2+3x+5)=1

解方程:x^2 + 3x -√(x^2 + 3x + 5) = 1

设y = x^2 + 3x，则
y - √(y + 5) = 1
y - 1 = √(y + 5)
y^2 -2y + 1 = y + 5
y^2 - 3y - 4 = 0
(y - 4)(y + 1) = 0
y1 = 4
y2 = -1

1、当y1 = 4时
x^2 + 3x - 4 = 0
(x + 4)(x - 1) = 0
x1 = -4
x2 = 1

2、当y2 = -1时
x^2 + 3x + 1 = 0
x^2 + 3x + (3/2)^2 - (3/2)^2 + 1 = 0
(x + 3/2)^2 = 5/4
x + 3/2 = ±√5/2
x3 = -3/2 + √5/2
x4 = -3/2 - √5/2

经检验，x1 = -4，x2 = 1，x3 = -3/2 + √5/2和x4 = -3/2 - √5/2都是原方程的根。