Question

20 баллов!!!
Решите уравнение

Answer 1

1. (3х-1)(х+4)=-4
3х²+12х-х-4=-4
3х²+11х-4+4=0
3х²+11х=0
х(3х+11)=0
х1=0
х2=-11/3=
$= - 3 \frac{2}{3}$

2. (2х-1)²-6(6-х)=2х
4х²-4х+1-36+6х=2х
4х²+2х-35-2х=0
4х²-35=0
4х²=35
х²=35/4
$x_1 = \sqrt{ \frac{35}{4} } = \frac{ \sqrt{35} }{2}$
$x_{2} = - \sqrt{ \frac{35}{4} } = - \frac{ \sqrt{35} }{2}$
3. (х+2)(х-3)-(х-5)(х+5)=х²-х
х²-3х+2х-6-(х²-25)=х²-х
х²-х-6-х²+25-х²+х=0
-х²+19=0
19=х²
х1=√19
х2=-√19

4. (2х-5)(х+2)=18
2х²+4х-5х-10-18=0
2х²-х-28=0
Д=1-4*2*28=225=15²
$x_1 = \frac{1 - 15}{2 \times 2} = \frac{ - 14}{4} = - \frac{7}{2} = - 3.5$
$x_2 = \frac{1 + 15}{2 \times 2} = \frac{16}{4} = 4$

5. (4х-3)²+(3х-1)(3х+1)=9
16х²-24х+9+9х²-1-9=0
25х²-24х-1=0
(а=25, b=-24, c=-1
a+b+c=25-24-1=0 → x1=1, x2=c/a)
х1=1
х2=-1/25

6.
$\frac{2x - 3}{9} + \frac{x - 1}{5} = 2$
умножим уравнение на 45
$45 \times \frac{2x - 3}{9} +45 \times \frac{x - 1}{5} = 45 \times 2 \\5(2x - 3) + 9(x - 1) = 90 \\ 10x - 15 + 9x - 9 = 90 \\ 19x - 24 = 90 \\19x = 90 + 24 \\ 19x = 114 \\ x = \frac{114}{19} \\ x = 6$