4) 3,(7)
Пусть x = 3,77 ... , тогда 10x = 37,77 ...
10x - x = 37,77 ... - 3,77 ...
9x = 34
![x= \frac{34}{9} =3 \frac{7}{9} \\\\3,(7)=3 \frac{7}{9}](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B34%7D%7B9%7D+%3D3+%5Cfrac%7B7%7D%7B9%7D+%5C%5C%5C%5C3%2C%287%29%3D3+%5Cfrac%7B7%7D%7B9%7D+)
β - угол четвёртой четверти значит Cosβ > 0
![Cos \beta = \sqrt{1-Sin ^{2} \beta } = \sqrt{1-(- \frac{12}{13}) ^{2} }= \sqrt{1- \frac{144}{169} }= \sqrt{ \frac{25}{169} }= \frac{5}{13}\\\\tg \beta = \frac{Sin \beta }{Cos \beta } = \frac{- \frac{12}{13} }{ \frac{5}{13} } =- \frac{12}{5}=-2,4 \\\\tg2 \beta = \frac{2tg \beta }{1-tg ^{2} \beta }=](https://tex.z-dn.net/?f=Cos+%5Cbeta+%3D+%5Csqrt%7B1-Sin+%5E%7B2%7D+%5Cbeta++%7D+%3D+%5Csqrt%7B1-%28-+%5Cfrac%7B12%7D%7B13%7D%29+%5E%7B2%7D++%7D%3D+%5Csqrt%7B1-+%5Cfrac%7B144%7D%7B169%7D+%7D%3D+%5Csqrt%7B+%5Cfrac%7B25%7D%7B169%7D+%7D%3D+%5Cfrac%7B5%7D%7B13%7D%5C%5C%5C%5Ctg+%5Cbeta+%3D+%5Cfrac%7BSin+%5Cbeta+%7D%7BCos+%5Cbeta+%7D+%3D+%5Cfrac%7B-+%5Cfrac%7B12%7D%7B13%7D+%7D%7B+%5Cfrac%7B5%7D%7B13%7D+%7D+%3D-+%5Cfrac%7B12%7D%7B5%7D%3D-2%2C4+%5C%5C%5C%5Ctg2+%5Cbeta+%3D+%5Cfrac%7B2tg+%5Cbeta+%7D%7B1-tg+%5E%7B2%7D+%5Cbeta++%7D%3D+++)
![= \frac{2*(-2,4)}{1-(-2,4) ^{2} }= \frac{-4,8}{1-5,76}= \frac{-4,8}{-4,76}= \frac{120}{119}=1 \frac{1}{119}](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B2%2A%28-2%2C4%29%7D%7B1-%28-2%2C4%29+%5E%7B2%7D+%7D%3D+%5Cfrac%7B-4%2C8%7D%7B1-5%2C76%7D%3D+%5Cfrac%7B-4%2C8%7D%7B-4%2C76%7D%3D+%5Cfrac%7B120%7D%7B119%7D%3D1+%5Cfrac%7B1%7D%7B119%7D++++)
Y`=3x²-16x+16=0
D=256-192=64
x=(16-8)/6=4/3∉[3,5;15]
x2=(16+8)/6=4∈[3,5;15]
y(3,5)=343/8-78+56+17=303/8=37,875
y(4)=64-128+64+17=17 наим
y(15)=3375-200+240+17=3432
1)a(x-y)+4(x-y)=(х-у)(а+4)
2) 3x-3y+ax-ay=3(х-у)+а(х-у)=(х-у)(3+а)