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

Question

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

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Answer 1 · 2016-06-10T14:39:25

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

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