докажем при помощи мат индукции
так как
![a_{n}](https://tex.z-dn.net/?f=a_%7Bn%7D)
кратно
![9](https://tex.z-dn.net/?f=9)
, надо доказать что
![2^{2n}+2](https://tex.z-dn.net/?f=+2%5E%7B2n%7D%2B2)
кратно
![3](https://tex.z-dn.net/?f=+3)
что верно , так как
![2^{2n}+2](https://tex.z-dn.net/?f=2%5E%7B2n%7D%2B2)
уже содержит множитель
![3](https://tex.z-dn.net/?f=3)
либо
![a_{n+1}=4^{n+1}+6n+6-1=4*4^n+24n-4-18n+9\\ a_{n+1}=4*a_{n}-9(2n-1)](https://tex.z-dn.net/?f=+a_%7Bn%2B1%7D%3D4%5E%7Bn%2B1%7D%2B6n%2B6-1%3D4%2A4%5En%2B24n-4-18n%2B9%5C%5C%0A++a_%7Bn%2B1%7D%3D4%2Aa_%7Bn%7D-9%282n-1%29)
то есть кратно
Сначало вытащим Y за скобку
y(1-4\7)=4.2
y=4.2\(1-4\7)
y=4.2\(3\7)
y=9.8
Log0,6_(2x-1) < log0,6_x;
0,6 < 1;
⇒2x-1 > x;
2x - x > 1;
x > 0,5
ОДЗ : x + 1 ≥ 0 ⇒ x ≥ - 1
![14*4^{\sqrt{x+1}}+3*14^{\sqrt{x+1}}-2*49^{\sqrt{x+1}}=0\\\\\frac{14*4^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}+\frac{3*14^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}-\frac{2*49^{\sqrt{x+1}}}{4^{\sqrt{x+1}}}=0\\\\14+3*(\frac{7}{2})^{\sqrt{x+1}}-2*[( \frac{7}{2})^{\sqrt{x+1}}]^{2}=0\\\\(\frac{7}{2})^{\sqrt{x+1}}=m,m>0\\\\14+3m-2m^{2}=0\\\\2m^{2}-3m-14=0\\\\D=(-3)^{2}-4*2*(-14)=9+112=121=11^{2}\\\\m_{1}=\frac{3+11}{4}=\frac{7}{2}\\\\m_{2}=\frac{3-11}{4}=-2<0-neyd\\\\(\frac{7}{2})^{\sqrt{x+1}}=\frac{7}{2}](https://tex.z-dn.net/?f=14%2A4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%2B3%2A14%5E%7B%5Csqrt%7Bx%2B1%7D%7D-2%2A49%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D0%5C%5C%5C%5C%5Cfrac%7B14%2A4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D%7B4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D%2B%5Cfrac%7B3%2A14%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D%7B4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D-%5Cfrac%7B2%2A49%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D%7B4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%7D%3D0%5C%5C%5C%5C14%2B3%2A%28%5Cfrac%7B7%7D%7B2%7D%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D-2%2A%5B%28%20%5Cfrac%7B7%7D%7B2%7D%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D%5D%5E%7B2%7D%3D0%5C%5C%5C%5C%28%5Cfrac%7B7%7D%7B2%7D%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3Dm%2Cm%3E0%5C%5C%5C%5C14%2B3m-2m%5E%7B2%7D%3D0%5C%5C%5C%5C2m%5E%7B2%7D-3m-14%3D0%5C%5C%5C%5CD%3D%28-3%29%5E%7B2%7D-4%2A2%2A%28-14%29%3D9%2B112%3D121%3D11%5E%7B2%7D%5C%5C%5C%5Cm_%7B1%7D%3D%5Cfrac%7B3%2B11%7D%7B4%7D%3D%5Cfrac%7B7%7D%7B2%7D%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B3-11%7D%7B4%7D%3D-2%3C0-neyd%5C%5C%5C%5C%28%5Cfrac%7B7%7D%7B2%7D%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D%5Cfrac%7B7%7D%7B2%7D)
![\sqrt{x+1}=1\\\\x+1=1\\\\x=0\\\\Otvet:\boxed{0}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B1%7D%3D1%5C%5C%5C%5Cx%2B1%3D1%5C%5C%5C%5Cx%3D0%5C%5C%5C%5COtvet%3A%5Cboxed%7B0%7D)