Question

giải hệ phương trình:

\(\left\{{}\begin{matrix}x+y+z=2\\2xy-z^2=4\end{matrix}\right.\)

Answer 1

Tham khảo

{x + y + z = 2
{2xy - z^2 = 4
<=> {z=2-y-x
       {z^2=2xy-4
<=>{z^2=4+y^2+x^2-4y+2xy-4x
      {z^2=2xy-4
=> 4+y^2+x^2-4y+2xy-4x=2xy-4
<=>8+y^2+x^2-4y-4x=0
<=> (x^2-4x+4)+(y^2-4y+4)=0
<=>(x-2)^2+(y-2)^2=0
<=>{(x-2)^2=0
      {(y-2)^2=0
<=>{ x=2
       {y=2
=>z=2-2-2=-2
vậy x=2,y=2,z=-2