《2025年零障碍导教导学案九年级数学全一册北师大版》

9. 解方程:$48x-4x^{2}=44$. 解:方程化为$4x^2 - 48x + 44 = 0$.
$x^2 - 12x + 11 = 0$.
$(x - 1)(x - 11) = 0$.
$x - 1 = 0$,或$x - 11 = 0$.
$x_1=$1,$x_2=$11.
10. 解方程:$200(1-x)^{2}=162$. 解:$(1 - x)^2=$0.81.
$1 - x = \pm\sqrt{0.81}$.
$1 - x = \pm$0.9.
$x = 1 \pm0.9$.
$x_1=$0.1,$x_2=$1.9.

答案： 9. 解:方程化为$4x^2 - 48x + 44 = 0$.
$x^2 - 12x + 11 = 0$.
$(x - 1)(x - 11) = 0$.
$x - 1 = 0$,或$x - 11 = 0$.
$x_1 = 1$,$x_2 = 11$.
10. 解:$(1 - x)^2 = 0.81$.
$1 - x = \pm\sqrt{0.81}$.
$1 - x = \pm0.9$.
$x = 1 \pm0.9$.
$x_1 = 0.1$,$x_2 = 1.9$.

11. (1)(2024·东莞月考)有一个密码程序系统,其原理如图所示,当输出为14时,输入的$x=$$-7$或$2$;
输入x→$x^{2}+5x$→输出
(2)若$(a^{2}+b^{2})^{2}-2(a^{2}+b^{2})-3=0$,则代数式$a^{2}+b^{2}$的值为$3$.

答案：
(1)$-7$或$2$
(2)$3$

12. 已知一元二次方程$x^{2}-10x+24=0$的两个根是菱形的两条对角线长,则这个菱形的面积为 (C)
A.6
B.10
C.12
D.24

答案： C

13. 解方程:$\frac {1}{2}x(x-1)=15$.
解:$x(x - 1) = 30$
$x^2 - x = 30$
$x^2 - x - 30 = 0$
$(x + 5)(x - 6) = 0$
$x + 5 = 0$,或$x - 6 = 0$
$x_1 = -5$,$x_2 = 6$
14. 解方程:$(8-2x)(6-2x)=24$.
解:原方程可化为$x^2 - 7x + 6 = 0$
$(x - 1)(x - 6) = 0$
$x - 1 = 0$,或$x - 6 = 0$
$x_1 = 1$,$x_2 = 6$

答案： 13. 解:$x(x - 1) = 30$.
$x^2 - x = 30$.
$x^2 - x - 30 = 0$.
$(x + 5)(x - 6) = 0$.
$x + 5 = 0$,或$x - 6 = 0$.
$x_1 = -5$,$x_2 = 6$.
14. 解:原方程可化为
$x^2 - 7x + 6 = 0$,
$(x - 1)(x - 6) = 0$,
$x - 1 = 0$,或$x - 6 = 0$.
$x_1 = 1$,$x_2 = 6$.