-х² + х + 42 = 0
х² - х - 42 = 0
По теореме Виета: х₁ = -6
х₂ = 7
7,(2)=7,222....
72,222..-7,2=65
65/(10-1)=65/9
23,(25)=23,252525...
2325,2525...-23,2525...=2302
2302/(100-1)=2302/99
1) a/m² + a²/m²=a+a²/m²
2) m²/a² + m/a= m²/a² + am/a²=m²+am/a²=m(m+a)/a²
3) a+a²/m² : m(m+a)/a² = a+a²/m² * a²/m(m+a)=a³+a⁴/m⁴+am³
1) (cos²2α+2sin2αcos2α+sin²2α)- (2sin4α*cos4α):2cos4α=1+sin4α-sin4α=1
3)2cos²2α-cos4α=2cosα2α-cos²2α+sin²2α=cos²2α+sin²2α=1
![\frac{sin2 \alpha }{1-2sin ^{2} \alpha } = \frac{sin2 \alpha }{cos ^{2} \alpha +sin ^{2} \alpha -2sin ^{2} \alpha } = \frac{sin2 \alpha }{cos \alpha ^{2} -sin ^{2} \alpha } = \frac{sin2 \alpha }{cos2 \alpha } =tg2 \alpha](https://tex.z-dn.net/?f=+%5Cfrac%7Bsin2+%5Calpha+%7D%7B1-2sin+%5E%7B2%7D+%5Calpha++%7D+%3D+%5Cfrac%7Bsin2+%5Calpha+%7D%7Bcos+%5E%7B2%7D+%5Calpha+%2Bsin+%5E%7B2%7D++%5Calpha+-2sin+%5E%7B2%7D++%5Calpha++%7D+%3D+%5Cfrac%7Bsin2+%5Calpha+%7D%7Bcos++%5Calpha+%5E%7B2%7D+-sin+%5E%7B2%7D+%5Calpha++%7D+%3D+%5Cfrac%7Bsin2+%5Calpha+%7D%7Bcos2+%5Calpha+%7D+%3Dtg2+%5Calpha+)
преобразуем правую часть
![\frac{2tg \alpha }{1-tg ^{2} \alpha } =tg2 \alpha](https://tex.z-dn.net/?f=+%5Cfrac%7B2tg+%5Calpha+%7D%7B1-tg+%5E%7B2%7D++%5Calpha+%7D+%3Dtg2+%5Calpha+)
tg2α=tg2α тождество доказано