16/50 = 0,32=32(%) вероятность того, что ему попадется невыученный билет.
(a-b)(a+b)=a-b
![(\sqrt{x-13}+\sqrt{x+13})(\sqrt{x-13}-\sqrt{x+13})=\sqrt{x-13}^2-\sqrt{x+13}^2=x-13-x-13=-26](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx-13%7D%2B%5Csqrt%7Bx%2B13%7D%29%28%5Csqrt%7Bx-13%7D-%5Csqrt%7Bx%2B13%7D%29%3D%5Csqrt%7Bx-13%7D%5E2-%5Csqrt%7Bx%2B13%7D%5E2%3Dx-13-x-13%3D-26)
то есть
![(\sqrt{x-13}+\sqrt{x+13})(\sqrt{x-13}-\sqrt{x+13})=-26](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx-13%7D%2B%5Csqrt%7Bx%2B13%7D%29%28%5Csqrt%7Bx-13%7D-%5Csqrt%7Bx%2B13%7D%29%3D-26)
подставим в это выражение ![\sqrt{x-13}-\sqrt{x+13}=-1](https://tex.z-dn.net/?f=%5Csqrt%7Bx-13%7D-%5Csqrt%7Bx%2B13%7D%3D-1)
![-1*(\sqrt{x-13}+\sqrt{x+13})=-26](https://tex.z-dn.net/?f=-1%2A%28%5Csqrt%7Bx-13%7D%2B%5Csqrt%7Bx%2B13%7D%29%3D-26)
![\sqrt{x-13}+\sqrt{x+13}=26](https://tex.z-dn.net/?f=%5Csqrt%7Bx-13%7D%2B%5Csqrt%7Bx%2B13%7D%3D26)
Ответ: 26
1) (x+1) (x-x+1)=(x+1)(в квадрате)
2) (а-2) (а в квадрате + 2а+ 4)
2) (3х-у)в квадрате = (3х -у) (9х в квадрате-3ху+у в квадрате)
Все вроде бы правильно)
раскройте скобку с синусом по формуле sin(a+b)=sina*cosb+ cosa*sinb
![x^{4}+\frac{x^{4}}{1+x^{4}}+\frac{x^{4} }{(1+x^{4})^{2}}+\frac{x^{4}}{(1+x^{4})^{3}}+...}=x^{4} (1+\frac{1}{1+x^{4}}+\frac{1}{(1+x^{4})^{2}}+\frac{1}{(1+x^{4})^{3}}+...)](https://tex.z-dn.net/?f=x%5E%7B4%7D%2B%5Cfrac%7Bx%5E%7B4%7D%7D%7B1%2Bx%5E%7B4%7D%7D%2B%5Cfrac%7Bx%5E%7B4%7D%20%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B2%7D%7D%2B%5Cfrac%7Bx%5E%7B4%7D%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B3%7D%7D%2B...%7D%3Dx%5E%7B4%7D%20%281%2B%5Cfrac%7B1%7D%7B1%2Bx%5E%7B4%7D%7D%2B%5Cfrac%7B1%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B2%7D%7D%2B%5Cfrac%7B1%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B3%7D%7D%2B...%29)
То что в скобках - это бесконечно убывающая геометрическая прогрессия в которой b₁ = 1 , а q = 1/(1+x⁴).
Найдём сумму этой прогрессии :
![S=\frac{b_{1} }{1-q} =\frac{1}{1-\frac{1}{1+x^{4}}}=\frac{1}{\frac{1+x^{4}-1 }{1+x^{4}}}=\frac{1}{\frac{x^{4} }{1+x^{4}}}=\frac{1+x^{4} }{x^{4}}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Bb_%7B1%7D%20%7D%7B1-q%7D%20%3D%5Cfrac%7B1%7D%7B1-%5Cfrac%7B1%7D%7B1%2Bx%5E%7B4%7D%7D%7D%3D%5Cfrac%7B1%7D%7B%5Cfrac%7B1%2Bx%5E%7B4%7D-1%20%7D%7B1%2Bx%5E%7B4%7D%7D%7D%3D%5Cfrac%7B1%7D%7B%5Cfrac%7Bx%5E%7B4%7D%20%7D%7B1%2Bx%5E%7B4%7D%7D%7D%3D%5Cfrac%7B1%2Bx%5E%7B4%7D%20%7D%7Bx%5E%7B4%7D%7D)
Следовательно :
![x^{4}+\frac{x^{4} }{1+x^{4}}+\frac{x^{4}}{(1+x^{4})^{2}}=\frac{x^{4} }{(1+x^{4})^{3}}+... =x^{4}*\frac{1+x^{4}}{x^{4}}=1+x^{4} \\\\x=3\\\\1+x^{4}=1+3^{4}=1+81=82\\\\Otvet:\boxed{82}](https://tex.z-dn.net/?f=x%5E%7B4%7D%2B%5Cfrac%7Bx%5E%7B4%7D%20%7D%7B1%2Bx%5E%7B4%7D%7D%2B%5Cfrac%7Bx%5E%7B4%7D%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B2%7D%7D%3D%5Cfrac%7Bx%5E%7B4%7D%20%7D%7B%281%2Bx%5E%7B4%7D%29%5E%7B3%7D%7D%2B...%20%3Dx%5E%7B4%7D%2A%5Cfrac%7B1%2Bx%5E%7B4%7D%7D%7Bx%5E%7B4%7D%7D%3D1%2Bx%5E%7B4%7D%20%5C%5C%5C%5Cx%3D3%5C%5C%5C%5C1%2Bx%5E%7B4%7D%3D1%2B3%5E%7B4%7D%3D1%2B81%3D82%5C%5C%5C%5COtvet%3A%5Cboxed%7B82%7D)
2)
![y_{n}=\frac{13-n}{5n+8}\\\\y_{n}=\frac{5}{48}\\\\\frac{13-n}{5n+8}=\frac{5}{48}\\\\48(13-n)=5(5n+8)\\\\624-48n=25n+40\\\\-48n-25n=40-624\\\\-73n=-584\\\\n=8\\\\Otvet:\boxed{n=8}](https://tex.z-dn.net/?f=y_%7Bn%7D%3D%5Cfrac%7B13-n%7D%7B5n%2B8%7D%5C%5C%5C%5Cy_%7Bn%7D%3D%5Cfrac%7B5%7D%7B48%7D%5C%5C%5C%5C%5Cfrac%7B13-n%7D%7B5n%2B8%7D%3D%5Cfrac%7B5%7D%7B48%7D%5C%5C%5C%5C48%2813-n%29%3D5%285n%2B8%29%5C%5C%5C%5C624-48n%3D25n%2B40%5C%5C%5C%5C-48n-25n%3D40-624%5C%5C%5C%5C-73n%3D-584%5C%5C%5C%5Cn%3D8%5C%5C%5C%5COtvet%3A%5Cboxed%7Bn%3D8%7D)