2x-3y=3 / *2
3x+2y=24 / *3
4x-6y=6
9x+6y=72
-6y и 6y вычеркиваем
4х+9х=72+6
13х=78
х=6
12-3у=3
3у=9
у=3
Всё :легко и просто.
x^6-x^4-x^2+1=x^2(x^3-x^2-1)+1.
8b^3-1/27=216d^3-1/27=8b^3-1.(2b-1)(4b^2+2b+1).
![\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
А-множество двузначных чисел кратных 11
А={11;22;33;44;55;66;77;88;99}
Жауабында қанша шығуы керек көріңіз