10-4x =0 -4x= -10 x=10/4 x=2,5 3x-1=5 3x=5+1 3x= 6 x=6/3 x=2
<span>log4(7-x)^2 + log4(x+9)^2=4+log4(x+9)^2
</span><span>log4(7-x)^2 + log4(x+9)^2=log4 256+log4(x+9)^2
</span>2log4 (7-x) + 2log4 (x+9) = 2log4 16 + 2log4 (x+9) |:2
log4 (7-x)(x+9) = log4 16(x+9)
<span>(7-x)(x+9) = 16(x+9)
</span><span>(7-x)(x+9) - 16(x+9) = 0
</span>(x + 9) (7 - x - 16) = 0
x + 9 = 0 или - 9 - x = 0
x = -9 x = -9
Ответ -9
Матрица А записана справа по строчкам. Это задача на нахождение значения матричного многочлена.
Аналогично значению функции в точке, только действия другие.
Находим
![A^{2}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1\cdot1-2\cdot0&1\cdot(-2)-2\cdot3\\0\cdot1+3\cdot0&0\cdot(-2)+3\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ccdot1-2%5Ccdot0%261%5Ccdot%28-2%29-2%5Ccdot3%5C%5C0%5Ccdot1%2B3%5Ccdot0%260%5Ccdot%28-2%29%2B3%5Ccdot3%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-8%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D)
Находим
![A^{3}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right] \cdot \left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\\\\ \left[\begin{array}{cc}1\cdot1-8\cdot0&1\cdot(-2)-8\cdot3\\0\cdot1+9\cdot0&0\cdot(-2)+9\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-26\\0&27\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B3%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-8%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D+%5Ccdot+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D+%3D%5C%5C%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ccdot1-8%5Ccdot0%261%5Ccdot%28-2%29-8%5Ccdot3%5C%5C0%5Ccdot1%2B9%5Ccdot0%260%5Ccdot%28-2%29%2B9%5Ccdot3%5Cend%7Barray%7D%5Cright%5D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-26%5C%5C0%2627%5Cend%7Barray%7D%5Cright%5D)
Тогда
![f(A)=3\cdot A^3-2\cdot A+4\cdot E=3\cdot\left[\begin{array}{cc}1&-26\\0&27\end{array}\right] -2\cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right]+4\cod\left[\begin{array}{cc}1&0\\0&1\end{array}\right]=\\\\ =\left[\begin{array}{cc}3\cdot1-2\cdot1+4\cdot1&3\cdot(-26)-2\cdot(-2)+4\cdot0\\3\cdot0-2\cdot0+4\cdot0&3\cdot27-2\cdot3+4\cdot1\end{array}\right]=\left[\begin{array}{cc}5&-74\\0&79\end{array}\right]](https://tex.z-dn.net/?f=f%28A%29%3D3%5Ccdot+A%5E3-2%5Ccdot+A%2B4%5Ccdot+E%3D3%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-26%5C%5C0%2627%5Cend%7Barray%7D%5Cright%5D+-2%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%2B4%5Ccod%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%5C%5C+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%5Ccdot1-2%5Ccdot1%2B4%5Ccdot1%263%5Ccdot%28-26%29-2%5Ccdot%28-2%29%2B4%5Ccdot0%5C%5C3%5Ccdot0-2%5Ccdot0%2B4%5Ccdot0%263%5Ccdot27-2%5Ccdot3%2B4%5Ccdot1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-74%5C%5C0%2679%5Cend%7Barray%7D%5Cright%5D)
1 1. 2у
(--------------- - --------- ) : ----------- =
х²-2ху+у² х²-у² ху+х²
1. 1. 1. 1
--------------- - ---------- = -------- - --------------- =
х²-2ху+у² х²-у² (х-у)² (х-у)(х+у)
х+у-х+у. 2у
------------------- = --------------------
(х-у)(х-у)(х+у) (х-у)(х-у)(х+у)
2у. 2у
-------------------- : ---------- =
(х-у)(х-у)(х+у) ху+х²
2у. х(у+х). х
-------------------- : ---------- = ---------------
(х-у)(х-у)(х+у) 2у. (х-у)²
3 ответ