Question

Solve the following system. x - y = 4 x y = 2 what is the solution of the system?

Answer 1

Hello,


`\left \{ {{x-y=4} \atop {xy=2}} \right \\\\ \left \{ {{x=4+y} \atop {(4+y)y=2}} \right \\\\ \left \{ {{x=4+y} \atop {y^2+4y-2=0}} \right. \\\\ \Delta=4^2-4*1*(-2)=24=(2 √(6) )^2\\\\ y= (-4+2 √(6) )/(2)\ or\ y= (-4-2 √(6) )/(2)\\\\ y= -2+√(6) \ or\ y= -2- √(6)\\ \boxed{Sol=\{ (2+ √(6) ,-2+√(6) ),(2- √(6) ,-2-√(6) )\} }`