<u>x-4 </u> - <u>2x+1 </u> =3
6 3
x-4 -2(2x+1)=3*6
x-4-4x-2=18
-3x=18+6
-3x=24
x= -8
Ответ: -8
Log 7^-1(x+10)+log√7/7(x+4)+2>0
-log7(x+10)+log7^-1/2(x+4)+2>0
-log7(x+10)-2log7(x+4)+2>0
{x+10>0, x>-10
x+4>0, x>-4
ответ:(-4;+∞)
1)10x²+13x-3=10(x+6/20)(x+1)=(10x+3)(x+1)
10x²+13x-3=0 Д=169+120=49
x1=(-13+7)/10*2=-6/20
x2=(-13-7)/20=-1
2)8х²<span>+34х+21=8(x+3/4)(x+14/4)=(4x+3)(2x+7)
</span>8х²+34х+21=0 Д=1156-32*21=484
x1=(-34+22)/16=-12/16=-3/4
x2=(-34-22)/16=-14/4
Неопределённость ∞/∞ раскрываем делением числителя и знаменателя на эн в максимальной степени, т.е. на
![n^4](https://tex.z-dn.net/?f=n%5E4)
![\lim_{n \to \infty} \frac{n^4+5n^2-1}{10n^3-3n+2}= \lim_{n \to \infty} \frac{1+ \frac{5}{n^2}- \frac{1}{n^4} }{ \frac{10}{n} - \frac{3}{n^3} + \frac{2}{n^4} }=\frac{1+ \frac{5}{oo^2}- \frac{1}{oo^4} }{ \frac{10}{oo} - \frac{3}{oo^3} + \frac{2}{oo^4} }= \\ \\ =\frac{1+ 0-0}{0-0+0}= \frac{1}{0} =oo](https://tex.z-dn.net/?f=+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7Bn%5E4%2B5n%5E2-1%7D%7B10n%5E3-3n%2B2%7D%3D+%5Clim_%7Bn+%5Cto+%5Cinfty%7D++%5Cfrac%7B1%2B+%5Cfrac%7B5%7D%7Bn%5E2%7D-+%5Cfrac%7B1%7D%7Bn%5E4%7D+%7D%7B+%5Cfrac%7B10%7D%7Bn%7D+-+%5Cfrac%7B3%7D%7Bn%5E3%7D+%2B+%5Cfrac%7B2%7D%7Bn%5E4%7D+%7D%3D%5Cfrac%7B1%2B+%5Cfrac%7B5%7D%7Boo%5E2%7D-+%5Cfrac%7B1%7D%7Boo%5E4%7D+%7D%7B+%5Cfrac%7B10%7D%7Boo%7D+-+%5Cfrac%7B3%7D%7Boo%5E3%7D+%2B+%5Cfrac%7B2%7D%7Boo%5E4%7D+%7D%3D+%5C%5C++%5C%5C+%3D%5Cfrac%7B1%2B+0-0%7D%7B0-0%2B0%7D%3D+%5Cfrac%7B1%7D%7B0%7D+%3Doo)
(бесконечность)