2)a2+6ab+9b2-9a2-6ab+b2= 8a^2+10b^2
= решение = решение = решение = решение = решение =
Найдем, какие значение принимает 7а:
![\displaystyle \frac{7}5\ \textless \ a\ \textless \ 3.5\\\\\frac{7*7}5\ \textless \ 7a\ \textless \ \frac{7*7}2\\\\\frac{49}5\ \textless \ 7a\ \textless \ \frac{49}2](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7B7%7D5%5C+%5Ctextless+%5C++a%5C+%5Ctextless+%5C++3.5%5C%5C%5C%5C%5Cfrac%7B7%2A7%7D5%5C+%5Ctextless+%5C+7a%5C+%5Ctextless+%5C+%5Cfrac%7B7%2A7%7D2%5C%5C%5C%5C%5Cfrac%7B49%7D5%5C+%5Ctextless+%5C+7a%5C+%5Ctextless+%5C+%5Cfrac%7B49%7D2)
Значения, которые принимает 2b:
![\displaystyle -2,5\ \textless \ b \ \textless \ - \frac{1}3\\\\-\frac{5*2}2\ \textless \ 2b\ \textless \ -\frac{2}3\\\\-5\ \textless \ 2b\ \textless \ -\frac{2}3](https://tex.z-dn.net/?f=%5Cdisplaystyle+-2%2C5%5C+%5Ctextless+%5C++b+%5C+%5Ctextless+%5C++-+%5Cfrac%7B1%7D3%5C%5C%5C%5C-%5Cfrac%7B5%2A2%7D2%5C+%5Ctextless+%5C+2b%5C+%5Ctextless+%5C+-%5Cfrac%7B2%7D3%5C%5C%5C%5C-5%5C+%5Ctextless+%5C+2b%5C+%5Ctextless+%5C+-%5Cfrac%7B2%7D3)
А теперь 7a-2b:
![\displaystyle \frac{49}5-(-5)\ \textless \ 7a-2b\ \textless \ \frac{49}2-\bigg(-\frac{2}3\bigg)\\\\\\\frac{49}5+\frac{5*5}5\ \textless \ 7a-2b\ \textless \ \frac{49*3}{6}+\frac{2*2}{6}\\\\\\\frac{74}{5}\ \textless \ 7a-2b\ \textless \ \frac{151}{6}\\\\\\14.8\ \textless \ 7a-2b\ \textless \ 25.1(6)\\\\\\15,\,\,\,16,\,\,\,17,\,\,\,18,\,\,\,19,\,\,\,20,\,\,\,21,\,\,\,22,\,\,\,23,\,\,\,24,\,\,\,25\\\\\\\text{OTBET}:\,\,11](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7B49%7D5-%28-5%29%5C+%5Ctextless+%5C+7a-2b%5C+%5Ctextless+%5C+%5Cfrac%7B49%7D2-%5Cbigg%28-%5Cfrac%7B2%7D3%5Cbigg%29%5C%5C%5C%5C%5C%5C%5Cfrac%7B49%7D5%2B%5Cfrac%7B5%2A5%7D5%5C+%5Ctextless+%5C+7a-2b%5C+%5Ctextless+%5C+%5Cfrac%7B49%2A3%7D%7B6%7D%2B%5Cfrac%7B2%2A2%7D%7B6%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B74%7D%7B5%7D%5C+%5Ctextless+%5C+7a-2b%5C+%5Ctextless+%5C+%5Cfrac%7B151%7D%7B6%7D%5C%5C%5C%5C%5C%5C14.8%5C+%5Ctextless+%5C+7a-2b%5C+%5Ctextless+%5C+25.1%286%29%5C%5C%5C%5C%5C%5C15%2C%5C%2C%5C%2C%5C%2C16%2C%5C%2C%5C%2C%5C%2C17%2C%5C%2C%5C%2C%5C%2C18%2C%5C%2C%5C%2C%5C%2C19%2C%5C%2C%5C%2C%5C%2C20%2C%5C%2C%5C%2C%5C%2C21%2C%5C%2C%5C%2C%5C%2C22%2C%5C%2C%5C%2C%5C%2C23%2C%5C%2C%5C%2C%5C%2C24%2C%5C%2C%5C%2C%5C%2C25%5C%5C%5C%5C%5C%5C%5Ctext%7BOTBET%7D%3A%5C%2C%5C%2C11)
х га - площадь целинных земель
(174 - х) га - площадь остальных земель
30 х центнеров - с целинных земель
22 (174 - х) ц - с остальных земель
30 х + 22 (174 - х) = 4556
30 х + 3828 - 22 х = 4556
30 х - 22 х = 4556 - 3828
8 х = 728
х = 728/8
х = 91
Ответ: целинных земель было освоено 91 га
<span>1) (1+ ctg</span>β<span>)</span>²<span>+ (1 - ctg</span>β<span> )</span>²=1+2ctgβ+ctg²β+1-2ctgβ+ctg²β=
=2+2ctg²β=2(1+ctg²β)=1/sin²β;<span>
2) </span>
![tgx+ \frac{cosx}{1+sinx} = \frac{tgx(1+sinx)+cosx}{1+sinx} = \frac{tgx+ \frac{sin ^{2}x }{cosx}+cosx }{1+sinx}= \frac{sinx+sin ^{2}x+cos^{2}x}{cosx}* \\ * \frac{1}{1+sinx}= \frac{1+sinx}{cosx} * \frac{1}{1+sinx}= \frac{1}{cosx}; \\](https://tex.z-dn.net/?f=tgx%2B+%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D+%3D+%5Cfrac%7Btgx%281%2Bsinx%29%2Bcosx%7D%7B1%2Bsinx%7D+%3D+%5Cfrac%7Btgx%2B+%5Cfrac%7Bsin+%5E%7B2%7Dx+%7D%7Bcosx%7D%2Bcosx+%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7Bsinx%2Bsin+%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%7D%7Bcosx%7D%2A+%5C%5C+%2A+%5Cfrac%7B1%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7B1%2Bsinx%7D%7Bcosx%7D+%2A+%5Cfrac%7B1%7D%7B1%2Bsinx%7D%3D+%5Cfrac%7B1%7D%7Bcosx%7D%3B+%5C%5C+++++)
<span>
3) </span>
![\frac{cos \beta }{1-sin \beta}+ \frac{1-sin \beta }{cos \beta }= \frac{cos^{2} \beta +1-2sin \beta +sin^{2} \beta }{(1-sin \beta )cos \beta } = \frac{2(1-sin \beta )}{(1-sin \beta )cos \beta }= \frac{2}{cos \beta };](https://tex.z-dn.net/?f=+%5Cfrac%7Bcos+%5Cbeta+%7D%7B1-sin+%5Cbeta%7D%2B+%5Cfrac%7B1-sin+%5Cbeta+%7D%7Bcos+%5Cbeta+%7D%3D+%5Cfrac%7Bcos%5E%7B2%7D+%5Cbeta++%2B1-2sin+%5Cbeta+%2Bsin%5E%7B2%7D++%5Cbeta+%7D%7B%281-sin+%5Cbeta+%29cos+%5Cbeta+%7D++%3D+%5Cfrac%7B2%281-sin+%5Cbeta+%29%7D%7B%281-sin+%5Cbeta+%29cos+%5Cbeta+%7D%3D+%5Cfrac%7B2%7D%7Bcos+%5Cbeta+%7D%3B+++)
<span>
4) </span>
![\frac{1+tg \alpha }{1+ctg \alpha } = \frac{cos \alpha+sin \alpha }{cos \alpha } * \frac{sin \alpha }{sin \alpha +cos \alpha }= \frac{sin \alpha }{cos \alpha } =tg \alpha .](https://tex.z-dn.net/?f=+%5Cfrac%7B1%2Btg+%5Calpha+%7D%7B1%2Bctg+%5Calpha+%7D+%3D+%5Cfrac%7Bcos+%5Calpha%2Bsin+%5Calpha++%7D%7Bcos+%5Calpha+%7D+%2A+%5Cfrac%7Bsin+%5Calpha+%7D%7Bsin+%5Calpha+%2Bcos+%5Calpha+%7D%3D+%5Cfrac%7Bsin+%5Calpha+%7D%7Bcos+%5Calpha+%7D+%3Dtg+%5Calpha+.+)