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1. 通过直接求
平方根
来解一元二次方程的方法叫做直接开平方法.
答案：
平方根
2. 如果一个一元二次方程具有$(x + h)^2 = k$(h,k为常数,$k\geq0$)的形式,那么可以用
直接开平方
法求解.
答案：
直接开平方
1. 方程$x^2 = 3$的根是 (
A.$x_1 = x_2 = 3$
B.$x_1 = x_2 = \sqrt{3}$
C.$x_1 = x_2 = -\sqrt{3}$
D.$x_1 = \sqrt{3},x_2 = -\sqrt{3}$
D
)A.$x_1 = x_2 = 3$
B.$x_1 = x_2 = \sqrt{3}$
C.$x_1 = x_2 = -\sqrt{3}$
D.$x_1 = \sqrt{3},x_2 = -\sqrt{3}$
答案：
D
2. 方程$(x + 1)^2 = 9$的根是 (
A.$x_1 = 8,x_2 = -10$
B.$x_1 = 10,x_2 = -8$
C.$x_1 = 2,x_2 = -4$
D.$x_1 = 4,x_2 = -2$
C
)A.$x_1 = 8,x_2 = -10$
B.$x_1 = 10,x_2 = -8$
C.$x_1 = 2,x_2 = -4$
D.$x_1 = 4,x_2 = -2$
答案：
C
3. 若方程$(x - 4)^2 = a$有实数解,则a的取值范围是 (
A.$a\leq0$
B.$a\geq0$
C.$a ＞ 0$
D.$a ＜ 0$
B
)A.$a\leq0$
B.$a\geq0$
C.$a ＞ 0$
D.$a ＜ 0$
答案：
B
4. 用直接开平方法解下列方程:
(1)$x^2 = 36$; (2)$x^2 + 1 = 1.01$;
(3)$(4x - 1)^2 = 36$; (4)$2(x^2 + 1) = 10$;
(5)$(x + 1)(x - 1) = 3$; (6)$(x - 4)^2 = (5 - 2x)^2$.
(1)$x^2 = 36$; (2)$x^2 + 1 = 1.01$;
(3)$(4x - 1)^2 = 36$; (4)$2(x^2 + 1) = 10$;
(5)$(x + 1)(x - 1) = 3$; (6)$(x - 4)^2 = (5 - 2x)^2$.
答案：
4.
(1)$x_{1}=6,x_{2}=-6$.
(2)$x_{1}=0.1,x_{2}=-0.1$.
(3)$x_{1}=\frac {7}{4},x_{2}=-\frac {5}{4}$.
(4)$x_{1}=2,x_{2}=-2$.
(5)$x_{1}=2,x_{2}=-2$.
(6)$x_{1}=1,x_{2}=3$.
(1)$x_{1}=6,x_{2}=-6$.
(2)$x_{1}=0.1,x_{2}=-0.1$.
(3)$x_{1}=\frac {7}{4},x_{2}=-\frac {5}{4}$.
(4)$x_{1}=2,x_{2}=-2$.
(5)$x_{1}=2,x_{2}=-2$.
(6)$x_{1}=1,x_{2}=3$.
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