7*5^log(5)2=7*2=14
----------------------------
![\left\{\begin{array}{I}(x+y)^2+3(x+y)+2=0\\ (x-y)^2-5(x-y)+6=0 \end{array}}](https://tex.z-dn.net/?f=+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D%28x%2By%29%5E2%2B3%28x%2By%29%2B2%3D0%5C%5C+%28x-y%29%5E2-5%28x-y%29%2B6%3D0+%5Cend%7Barray%7D%7D+)
Решим первое уравнение системы относительно x+y, второе относительно x-y.
1)
![(x+y)^2+3(x+y)+2=0\\ D=9-8=1\\ (x+y)_1=\dfrac{-3+1}{2}=-1\\ (x+y)_2=\dfrac{-3-1}{2}=-2](https://tex.z-dn.net/?f=+%28x%2By%29%5E2%2B3%28x%2By%29%2B2%3D0%5C%5C+D%3D9-8%3D1%5C%5C+%28x%2By%29_1%3D%5Cdfrac%7B-3%2B1%7D%7B2%7D%3D-1%5C%5C++%28x%2By%29_2%3D%5Cdfrac%7B-3-1%7D%7B2%7D%3D-2++)
2)
![(x-y)^2-5(x-y)+6=0\\ D=25-24=1\\ (x-y)_1=\dfrac{5-1}{2}=2\\ (x-y)_2=\dfrac{5+1}{2}=3](https://tex.z-dn.net/?f=+%28x-y%29%5E2-5%28x-y%29%2B6%3D0%5C%5C+D%3D25-24%3D1%5C%5C+%28x-y%29_1%3D%5Cdfrac%7B5-1%7D%7B2%7D%3D2%5C%5C++%28x-y%29_2%3D%5Cdfrac%7B5%2B1%7D%7B2%7D%3D3++)
Получили совокупность четырех систем.
![\left[\begin{array}{I} \left\{\begin{array}{I} x+y=-1 \\ x-y=2 \end{array}} \\ \left\{\begin{array}{I} x+y=-1 \\ x-y=3 \end{array}} \\ \left\{\begin{array}{I} x+y=-2 \\ x-y=2 \end{array}} \\\left\{\begin{array}{I} x+y=-2 \\ x-y=3 \end{array}}\end{array}}](https://tex.z-dn.net/?f=+%5Cleft%5B%5Cbegin%7Barray%7D%7BI%7D+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-1++%5C%5C+x-y%3D2+%5Cend%7Barray%7D%7D++%5C%5C+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-1++%5C%5C+x-y%3D3+%5Cend%7Barray%7D%7D+%5C%5C+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-2++%5C%5C+x-y%3D2+%5Cend%7Barray%7D%7D+%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-2++%5C%5C+x-y%3D3+%5Cend%7Barray%7D%7D%5Cend%7Barray%7D%7D+++)
Решаем каждую.
1)
![+ \left\{\begin{array}{I} x+y=-1 \\ x-y=2 \end{array}}](https://tex.z-dn.net/?f=+%2B+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-1++%5C%5C+x-y%3D2+%5Cend%7Barray%7D%7D+)
![2x=1\\ x=\dfrac{1}{2} \ \Rightarrow \ y= -\dfrac{3}{2}](https://tex.z-dn.net/?f=+2x%3D1%5C%5C+x%3D%5Cdfrac%7B1%7D%7B2%7D+%5C+%5CRightarrow+%5C+y%3D+-%5Cdfrac%7B3%7D%7B2%7D++)
2)
![+ \left\{\begin{array}{I} x+y=-1 \\ x-y=3 \end{array}}](https://tex.z-dn.net/?f=++%2B+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-1++%5C%5C+x-y%3D3+%5Cend%7Barray%7D%7D++)
![2x=2\\ x=1 \ \Rightarrow \ y=-2](https://tex.z-dn.net/?f=+2x%3D2%5C%5C+x%3D1+%5C+%5CRightarrow+%5C+y%3D-2+)
3)
![+ \left\{\begin{array}{I} x+y=-2 \\ x-y=2 \end{array}}](https://tex.z-dn.net/?f=+%2B+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-2++%5C%5C+x-y%3D2+%5Cend%7Barray%7D%7D+)
![x=0 \ \Rightarrow \ y=-2](https://tex.z-dn.net/?f=+x%3D0+%5C+%5CRightarrow+%5C+y%3D-2+)
4)
![+ \left\{\begin{array}{I} x+y=-2 \\ x-y=3 \end{array}}](https://tex.z-dn.net/?f=+%2B+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%2By%3D-2++%5C%5C+x-y%3D3+%5Cend%7Barray%7D%7D+)
![2x=1\\ x=\dfrac{1}{2} \ \Rightarrow \ y=-\dfrac{5}{2}](https://tex.z-dn.net/?f=+2x%3D1%5C%5C+x%3D%5Cdfrac%7B1%7D%7B2%7D+%5C+%5CRightarrow+%5C+y%3D-%5Cdfrac%7B5%7D%7B2%7D+++)
Считаем произведения.
![x_1y_1=\dfrac{1}{2} \cdot (-\dfrac{3}{2})=-\dfrac{3}{4}\\ x_2y_2=1 \cdot (-2)=-2\\ x_3y_3=0 \cdot (-2) =0\\ x_4y_4=\dfrac{1}{2} \cdot (-\dfrac{5}{2})=-\dfrac{5}{4}](https://tex.z-dn.net/?f=+x_1y_1%3D%5Cdfrac%7B1%7D%7B2%7D++%5Ccdot+%28-%5Cdfrac%7B3%7D%7B2%7D%29%3D-%5Cdfrac%7B3%7D%7B4%7D%5C%5C+++x_2y_2%3D1+%5Ccdot+%28-2%29%3D-2%5C%5C+x_3y_3%3D0+%5Ccdot+%28-2%29+%3D0%5C%5C+x_4y_4%3D%5Cdfrac%7B1%7D%7B2%7D+%5Ccdot+%28-%5Cdfrac%7B5%7D%7B2%7D%29%3D-%5Cdfrac%7B5%7D%7B4%7D++++)
Таким образом, наименьшее значение xy=-2
Ответ: -2
2a²+a-6a-3=2a²-5a-3
...............................
1)cosa-sina*ctga= cos a - sin a *cos a/sin a=cosa - cos a= 0
2) cos^2a/1-sin a= 1-sin^2a/1-sin a=(1-sin a)(1+sin a) /1-sin a=1+sin a
1) у=<u> х+3</u>
√х²-1
х²-1>0
(x-1)(x+1)>0
x=1 x=-1
+ - +
----- -1 ------ 1 ------
\\\\\\ \\\\\\
x∈(-∞; -1)∨(1; ∞)
D(y)=(-∞; -1)∨(1; ∞) - область определения функции.
2.
1) у=<u>х²-1</u>
х²+1
у(-х)= <u>(-х)²-1 </u> = <u>х²-1 </u>
(-х)²+1 х²+1
Так как у(-х)=у(х), то функция четная.
2) у=5х³+3х
у(-х)=5(-х)³+3(-х)=-5х³-3х= - (5х³+3х)
Так как у(-х)= -у(х), то функция нечетная.
3) у=х²-2х+1
у(-х)=(-х)²-2(-х)+1=х²+2х+1
Так как у(-х)≠у(х)≠-у(х), то функция не является четной и нечетной.
6.
у=2х+1
2х=у-1
х=0,5у-0,5
у=0,5х-0,5 - обратная функция.
Точки для построения графиков:
у=2х+1 - прямая y=0.5x-0.5 - прямая
<u>х | 0 | 2 | </u> <u> х | 0 | 2 |</u>
y | 1 | 5 | y | -0.5 | 0.5 |