《2025年课时练作业与测评九年级数学上册冀教版》

1. 运用直接开平方法解方程.
(1) $(x + 2)^2 - 25 = 0$.
(2) $x^2 - 9 = 0$.

答案：
(1)$(x + 2)^{2} - 25 = 0$,$(x + 2)^{2} = 25$,$x + 2 = \pm 5$,
$x_1 = 3$,$x_2 = -7$.
(2)$x^{2} - 9 = 0$,$x^{2} = 9$,$x = \pm 3$,$x_1 = 3$,$x_2 = -3$.

2. 运用配方法解方程.
(1) $x^2 + 4x - 5 = 0$.
(2) $x^2 - 4x + 1 = 0$.

答案：
(1)$x^{2} + 4x - 5 = 0$,$x^{2} + 4x + 4 = 5 + 4$,$(x + 2)^{2} = 9$,
$x + 2 = \pm 3$,$x_1 = 1$,$x_2 = -5$.
(2)$x^{2} - 4x + 1 = 0$,$x^{2} - 4x + 4 = -1 + 4$,$(x - 2)^{2} = 3$,
$x - 2 = \pm \sqrt{3}$,$x_1 = \sqrt{3} + 2$,$x_2 = - \sqrt{3} + 2$.

3. 运用公式法解方程.
(1) $x^2 + 3x - 2 = 0$.
(2) $3x^2 + 8x - 3 = 0$.

答案：
(1)$x^{2} + 3x - 2 = 0$,$a = 1$,$b = 3$,$c = -2$,
$b^{2} - 4ac = 9 + 8 = 17$,$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} = \frac{-3 \pm \sqrt{17}}{2}$
$x_1 = \frac{-3 + \sqrt{17}}{2}$,$x_2 = \frac{-3 - \sqrt{17}}{2}$.
(2)$3x^{2} + 8x - 3 = 0$,$a = 3$,$b = 8$,$c = -3$,
$b^{2} - 4ac = 64 + 36 = 100$,
$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} = \frac{-8 \pm \sqrt{100}}{2 × 3}$,$x_1 = \frac{1}{3}$,$x_2 = -3$.

4. 运用因式分解法解方程.
(1) $x^2 - x - 6 = 0$.
(2) $x(5x + 4) - (4 + 5x) = 0$.

答案：
(1)$x^{2} - x - 6 = 0$,$(x + 2)(x - 3) = 0$,$x_1 = -2$,$x_2 = 3$.
(2)$x(5x + 4) - (4 + 5x) = 0$,$(5x + 4)(x - 1) = 0$,
$x_1 = -\frac{4}{5}$,$x_2 = 1$.