Solve the following system of equations: (x^2+y^2=29),(xy=-10)(x2+y2=29),(xy=10) ?

Solve the following system of equations:
[(1 " ", x^2+y^2=29),(2 " ", xy=-10)]?

1 Answer
Jun 10, 2016

The solutions are {-5,2},{-2,5},{2,-5},{5,-2}

Explanation:

Substituting for y = -10/x we have

x^4-29 x^2+100 = 0

Making z = x^2 and solving for z

z^2-29 z+100 = 0 and subsequently we have the solutions for x

x = {-5,-2,2,5}.

With the final solutions

{-5,2},{-2,5},{2,-5},{5,-2}

The attached figure shows the intersection points of

{x^2+y^2-20=0} nn {x y +10 = 0}

enter image source here