Question

{a^2+2b^2=6 {b^2-2a=-3 как решить систему

Answer 1

Объяснение:

$\left \{ {{a^2+2b^2=6} \atop {b^2-2a=-3}} \right. \ \ \ \ \left \{ {{a^2+2b^2=6} \atop {b^2=2a-3\ |*2}} \right. \ \ \ \ \left \{ {{a^2+2b^2=6} \atop {2b^2=4a-6}} \right.\ \ \ \ \left \{ {{a^2+4a-6=6} \atop {b^2-2a=-3}} \right. \ \ \ \ \left \{ {{a^2+4a-12=0} \atop {b^2-2a=-3}} \right. .$

$a^2+4a-12=0\\D=64\ \ \ \ \ \sqrt{D}=8\\ a_1=-6\ \ \ \ \Rightarrow\\b^2-2*(-6)=-3\\b^2+12=-3\\b^2=-15\\b\in\varnothing.\\a_2=2\ \ \ \ \Rightarrow\\b^2-2*2=-3\\b^2-4=-3\\b^2=1\\b_1=-1\ \ \ \ b_2=1.$

Ответ: (2;-1),   (2;1).