Задание 1. Коэффициенты только при х⁴
1*х + 2*х³*7*х + 3*х²*2*х² + 4*х*х³ = (1+14+6+4)*х⁴ = 25*х⁴
Задание 2.
Решаем методом Крамера.
![det=\left[\begin{array}{ccc}2&4&1\\3&-1&2\\1&-5&3\end{array}\right] = -28 \\ detX=\left[\begin{array}{ccc}5&4&1\\3&-1&2\\4&-5&3\end{array}\right] =20 \\ detY=\left[\begin{array}{ccc}2&5&1\\3&3&2\\1&4&3\end{array}\right] =-24 \\ detZ= \left[\begin{array}{ccc}2&4&5\\3&-1&3\\1&-5&4\end{array}\right] =-84](https://tex.z-dn.net/?f=++det%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%261%5C%5C3%26-1%262%5C%5C1%26-5%263%5Cend%7Barray%7D%5Cright%5D+%3D+-28+%5C%5C+detX%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%264%261%5C%5C3%26-1%262%5C%5C4%26-5%263%5Cend%7Barray%7D%5Cright%5D+%3D20+%5C%5C+++detY%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%261%5C%5C3%263%262%5C%5C1%264%263%5Cend%7Barray%7D%5Cright%5D+%3D-24+%5C%5C+detZ%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%265%5C%5C3%26-1%263%5C%5C1%26-5%264%5Cend%7Barray%7D%5Cright%5D+%3D-84 "det=\left[\begin{array}{ccc}2&4&1\\3&-1&2\\1&-5&3\end{array}\right] = -28 \\ detX=\left[\begin{array}{ccc}5&4&1\\3&-1&2\\4&-5&3\end{array}\right] =20 \\ detY=\left[\begin{array}{ccc}2&5&1\\3&3&2\\1&4&3\end{array}\right] =-24 \\ detZ= \left[\begin{array}{ccc}2&4&5\\3&-1&3\\1&-5&4\end{array}\right] =-84")
X = -20/28 = - 5/7, Y=-24/(-28) =6/7, Z=-28/(-84)=3
X+2*Y+Z= 4 - ОТВЕТ
Задание 3.
t = 4/(v+1) + 8/v = 1 - уравнение для времени.
Упрощаем
4*v + 8*(v+1) = v*(v+1)
Упрощаем
v² + v - 4*v - 8*v - 8 = 0
Получаем квадратное уравнение
v² - 11*v - 8 = 0
Решаем. Дискриминант D=153, X1 = 11.685 ≈ 11.69 - ОТВЕТ