![\frac{13}{225}=0,05(7)](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B225%7D%3D0%2C05%287%29)
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![\displaystyle \frac{6 cos^2x-5 \sqrt{2} cosx+2}{lg(tgx)}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Cfrac%7B6+cos%5E2x-5+%5Csqrt%7B2%7D+cosx%2B2%7D%7Blg%28tgx%29%7D%3D0+)
![\displaystyle ODZ:\\\\ \left \{ {{lg(tgx) \neq 0} \atop {tgx\ \textgreater \ 0}} \right. \\\\ \left \{ {{tgx \neq 1} \atop {x\in ( \pi n; \frac{ \pi }{2}+ \pi n) n\in Z}} \right. \\\\ \left \{ {{x \neq \frac{ \pi }{4}+ \pi n; n\in Z} \atop {x\in ( \pi n; \frac{ \pi }{2}+ \pi n); n\in Z}} \right.](https://tex.z-dn.net/?f=%5Cdisplaystyle+ODZ%3A%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Blg%28tgx%29+%5Cneq+0%7D+%5Catop+%7Btgx%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Btgx+%5Cneq+1%7D+%5Catop+%7Bx%5Cin+%28+%5Cpi+n%3B++%5Cfrac%7B+%5Cpi+%7D%7B2%7D%2B+%5Cpi+n%29+n%5Cin+Z%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bx+%5Cneq++%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B+%5Cpi+n%3B+n%5Cin+Z%7D+%5Catop+%7Bx%5Cin+%28+%5Cpi+n%3B++%5Cfrac%7B+%5Cpi+%7D%7B2%7D%2B+%5Cpi+n%29%3B+n%5Cin+Z%7D%7D+%5Cright.+)
дробь равна нулю когда числитель равен нулю
![\displaystyle 6cos^2x-5 \sqrt{2}cosx+2=0\\\\ cosx=t; |t|\ \textless \ 1\\\\D=25*2-4*6*2=50-48=2\\\\t_{1.2}= \frac{5 \sqrt{2}\pm \sqrt{2}}{12}\\\\t_1= \frac{ \sqrt{2}}{2}; t_2= \frac{ \sqrt{2}}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle+6cos%5E2x-5+%5Csqrt%7B2%7Dcosx%2B2%3D0%5C%5C%5C%5C+cosx%3Dt%3B+%7Ct%7C%5C+%5Ctextless+%5C+1%5C%5C%5C%5CD%3D25%2A2-4%2A6%2A2%3D50-48%3D2%5C%5C%5C%5Ct_%7B1.2%7D%3D+%5Cfrac%7B5+%5Csqrt%7B2%7D%5Cpm++%5Csqrt%7B2%7D%7D%7B12%7D%5C%5C%5C%5Ct_1%3D+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%3B+t_2%3D+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D+++)
![\displaystyle cosx= \frac{ \sqrt{2}}{2}\\\\x_{1.2}=\pm \frac{ \pi }{4}+2 \pi n; n\in Z\\\\x_1= \frac{ \pi }{4}+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+cosx%3D++%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5C%5Cx_%7B1.2%7D%3D%5Cpm++%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_1%3D+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+Z+++++)
не входит в ОДЗ
![\displaystyle x_2=- \frac{ \pi }{4}+2 \pi n; n\in z](https://tex.z-dn.net/?f=%5Cdisplaystyle+x_2%3D-+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B2+%5Cpi+n%3B+n%5Cin+z+)
не входит в ОДЗ
![\displaystyle cosx= \frac{ \sqrt{2}}{3}\\\\x_{3.4}=\pm arccos( \frac{ \sqrt{2}}{3})+2 \pi n; n\in Z\\\\x_3=- arccos( \frac{ \sqrt{2}}{3})+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+cosx%3D+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%5C%5C%5C%5Cx_%7B3.4%7D%3D%5Cpm+arccos%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%29%2B2+%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx_3%3D-+arccos%28+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%29%2B2+%5Cpi+n%3B+n%5Cin+Z+++)
не входит в ОДЗ
ОТВЕТ
![\displaystyle x_4=arccos \frac{ \sqrt{2}}{3}+2 \pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+x_4%3Darccos++%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B3%7D%2B2+%5Cpi+n%3B+n%5Cin+Z+)
Ответ:
Объяснение:
ответ на фото\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
8. 4√2-3√8+2√32=4√2-2√4×2+2√16×2=4√2-6√2+16√2=14√2