Question

Решите систему уравнений пожалуйста
9x^2-12xy+4y^2=9
x+2y=9​
только способом, по типу этого ( как на фото)

Answer 1

$\left \{ {{9x^{2}-12xy+4y^{2}=9 } \atop {x+2y=9}} \right.\\\\\left \{ {{x=9-2y} \atop {9(9-2y)^{2} -12y*(9-2y)+4y^{2}=9}} \right.\\\\\left \{ {{x=9-2y} \atop {9(81-36y+4y^{2}) -108y+24y^{2}+4y^{2}-9=0}} \right.\\\\\left \{ {{x=9-2y} \atop {729-324y+36y^{2}-108y+28y^{2}-9=0}} \right.\\\\\left \{ {{x=9-2y} \atop {64y^{2}-432y+720=0 }} \right.\\\\4y^{2}-27y+45=0\\\\D=(-27)^{2}-4*4*45=729-720=9=3^{2}$

$y_{1}=\frac{27-3}{8}=\frac{24}{8}=3\\\\y_{2}=\frac{27+3}{8}=\frac{30}{8}=3,75\\\\x_{1}=9-2*y_{1}=9-2*3=3\\\\x_{2}=9-2*y_{2}=9-2*3,75=9-7,5=1,5\\\\Otvet:\boxed{(3;3),(1,5;3,75)}$