√3sinx+cosx=√2
A=√3
B=1
C=корень квадратный( (√3)^2 + 1^2)= √4=2
2* (√3/2sinx + 1/2cosx)=√2
cosП/6*sinx + sinП/6*cosx=√2/2
sin(x + П/6) = √2/2
x + П/6= (-1)^n П/4 + Пn
x=-П/6 + (-1)^n П/4 + Пn
Xy^2 + y^3 = y^2 (x + y) = 3^2 * (97 + 3) = 9 * 100 = 900
Получаем систему уравнений
![\left \{ {{x - y = 4} \atop { x^{2} - y^{2} = 32}} \right.\left \{ {{x - y = 4} \atop {(x-y)(x+y) = 32}} \right. \left \{ {{x - y = 4} \atop {4(x+y) = 32}} \right.\left \{ {{x - y = 4} \atop {x+y = 8}} \right.\left \{ {{x = 4+y} \atop {x+y = 8}} \right. \left \{ {{x = 4+y} \atop {4+y+y = 8}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx+-+y+%3D+4%7D+%5Catop+%7B+x%5E%7B2%7D+-+y%5E%7B2%7D+%3D+32%7D%7D+%5Cright.%5Cleft+%5C%7B+%7B%7Bx+-+y+%3D+4%7D+%5Catop+%7B%28x-y%29%28x%2By%29+%3D+32%7D%7D+%5Cright.%0A%5Cleft+%5C%7B+%7B%7Bx+-+y+%3D+4%7D+%5Catop+%7B4%28x%2By%29+%3D+32%7D%7D+%5Cright.%5Cleft+%5C%7B+%7B%7Bx+-+y+%3D+4%7D+%5Catop+%7Bx%2By+%3D+8%7D%7D+%5Cright.%5Cleft+%5C%7B+%7B%7Bx+%3D+4%2By%7D+%5Catop+%7Bx%2By+%3D+8%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Bx+%3D+4%2By%7D+%5Catop+%7B4%2By%2By+%3D+8%7D%7D+%5Cright.)
![\left \{ {{x = 4+y} \atop {2y = 4}} \right. \left \{ {{x = 4+y} \atop {y = 2}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx+%3D+4%2By%7D+%5Catop+%7B2y+%3D+4%7D%7D+%5Cright.%0A%5Cleft+%5C%7B+%7B%7Bx+%3D+4%2By%7D+%5Catop+%7By+%3D+2%7D%7D+%5Cright.)
y = 2, значит x = 2+4 = 6
Ответ: y = 2, x = 6
5х-15-2х+14+14х+42=7
17х=-34
х=-2
{x+xy+y=11
{x²+xy+y²=19
19-11=8=x²+y²-x-y
11-8=3=x
11-3=8-3=5=x+y=>y=2
ответ x=3, y=2