Question

解下列方程 请大家帮忙讲解一下谢谢

(1)x^2-2根号3乘以x=0 (2)3x^2-6x=3 (3)3x(x-2x)=3 (4)3x^2-6x-3=0 (5)4x^2-121=0

Answer 1

1、0 或 2根号3 （提取x）
2、1加减根号2
Possible intermediate steps:
3 x^2-6 x = 3
Divide both sides by 3:
x^2-2 x = 1
Add 1 to both sides:
x^2-2 x+1 = 2
Factor the left hand side:
(x-1)^2 = 2
Take the square root of both sides:
abs(x-1) = sqrt(2)
Eliminate the absolute value:
x-1 = -sqrt(2) or x-1 = sqrt(2)
Add 1 to both sides:
x = 1-sqrt(2) or x-1 = sqrt(2)
Add 1 to both sides:
x = 1-sqrt(2) or x = 1+sqrt(2)
注：abs 绝旦颂埋对值 ，sqrt 平方根
3、无实数模蚂根、如果你学过复数看下面解题
Possible intermediate steps:
-3 x^2 = 3
Divide both sides by -3:
x^2 = -1
Take the square root of both sides:
x = -i or x = i
4、同（2）
5、正负二分之樱毁十一
Possible intermediate steps:
4 x^2-121 = 0
Add 121 to both sides:
4 x^2 = 121
Divide both sides by 4:
x^2 = 121/4
Take the square root of both sides:
x = -11/2 or x = 11/2
毕。