Question

розв'яжіть систему рівнянь {4x^2-2xy=-3 {y^2-2xy=12​

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\left \{ {{4x^2-2xy=-3} \atop {y^2-2xy=12}} \right.\Leftrightarrow\left \{ {{16x^2-8xy=-12} \atop {y^2-2xy=12}} \right. \\\\16x^2-10xy+y^2=0\\\\16x^2-8xy-2xy+y^2=0\\\\8x(2x-y)-y(8x-y)=0\\\\(2x-y)(8x-y)=0$

1)

$\displaystyle\\\left \{ {{2x-y=0} \atop 4x^2-2xy=-3{}} \right.;\left \{ {{y=2x} \atop {4x^2-2x*2x=-3}} \right. ;\left \{ {{y=2x} \atop {0\neq -3}} \right.$

нет решений

2)

$\displaystyle\\\left \{ {{8x-y=0} \atop {4x^2-2xy=-3}} \right. ;\left \{ {{y=8x} \atop {4x^2-2x*8x=-3}} \right. \\\\\\\left \{ {{y=8x} \atop {-12x^2=-3}} \right. ;\left \{ {{y=8x} \atop {x^2=\dfrac{1}{4} }} \right.;\left \{ {{y=8x} \atop {x=\pm\dfrac{1}{2} }} \right.$

$Otvet:(-0,5;-4)~(0,5;4)$