Question

Решите систему уравнений {xy+x^2=4 y=x+2

Answer 1

Ответ:

(1;3), (-2;0).

Объяснение:

$left { begin{array}{lcl} {{xy+x^{2} =4,} \ y={x+2};} end{array} right.Leftrightarrowleft { begin{array}{lcl} {{x(x+2)+x^{2}=4, } \ {y=x+2};} end{array} right.Leftrightarrowleft { begin{array}{lcl} {{x^{2}+2x+x^{2}  =4,} \ {y=x+2}} end{array} right.Leftrightarrow$

$left { begin{array}{lcl} {{2x^{2}+2x-4 =0,} \ {y=x+2;}} end{array} right.Leftrightarrowleft { begin{array}{lcl} {{x^{2}+x -2=0,} \ {y=x+2;}} end{array} right.Leftrightarrow$

$left { begin{array}{lcl} {{left [ begin{array}{lcl} {{x=1,} \ {x=-2,}} end{array} right.} \ {y=x+2;}} end{array} right.Leftrightarrow left [ begin{array}{lcl} {{left { begin{array}{lcl} {{x=1,} \ {y=3;}} end{array} right.} \ {left { begin{array}{lcl} {{x=-2,} \ {y=0.}} end{array} right.}} end{array} right.$