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}](https://tex.z-dn.net/?f=+%3D++-+3++%5Cfrac%7B2%7D%7B3%7D+)
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}](https://tex.z-dn.net/?f=x_1+%3D++%5Csqrt%7B+%5Cfrac%7B35%7D%7B4%7D+%7D++%3D++%5Cfrac%7B+%5Csqrt%7B35%7D+%7D%7B2%7D+)
![x_{2} = - \sqrt{ \frac{35}{4} } = - \frac{ \sqrt{35} }{2}](https://tex.z-dn.net/?f=x_%7B2%7D+%3D++-++%5Csqrt%7B+%5Cfrac%7B35%7D%7B4%7D+%7D++%3D++-++%5Cfrac%7B+%5Csqrt%7B35%7D+%7D%7B2%7D+)
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](https://tex.z-dn.net/?f=x_1+%3D+%5Cfrac%7B1+-+15%7D%7B2+%5Ctimes+2%7D++%3D++%5Cfrac%7B+-+14%7D%7B4%7D++%3D++-++%5Cfrac%7B7%7D%7B2%7D++%3D++-+3.5)
![x_2 = \frac{1 + 15}{2 \times 2} = \frac{16}{4} = 4](https://tex.z-dn.net/?f=x_2+%3D+%5Cfrac%7B1+%2B+15%7D%7B2+%5Ctimes+2%7D++%3D++%5Cfrac%7B16%7D%7B4%7D++%3D+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](https://tex.z-dn.net/?f=+%5Cfrac%7B2x+-+3%7D%7B9%7D++%2B++%5Cfrac%7Bx+-+1%7D%7B5%7D++%3D+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](https://tex.z-dn.net/?f=45+%5Ctimes++%5Cfrac%7B2x+-+3%7D%7B9%7D++%2B45+%5Ctimes+++%5Cfrac%7Bx+-+1%7D%7B5%7D++%3D+45+%5Ctimes+2+%5C%5C5%282x+-+3%29+%2B+9%28x+-+1%29+%3D+90+%5C%5C+10x+-+15+%2B+9x+-+9+%3D+90+%5C%5C+19x+-+24+%3D+90+%5C%5C19x+%3D+90+%2B+24+%5C%5C+19x+%3D+114+%5C%5C+x+%3D++%5Cfrac%7B114%7D%7B19%7D++%5C%5C+x+%3D+6)
При t>2.8 ответ будет >0
=>(следовательно) ответ будет положителен
при t=2.8 ответ будет равен 0
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