SOLUTION: x^2+y^2=12 xy=-3

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Question 815906: x^2+y^2=12
xy=-3
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Try y=-3%2Fx and substitute into the circle equation:
x%5E2%2B%28-3%2Fx%29%5E2=12
x%5E2%2B9%2F%28x%5E2%29=12
x%5E4%2B9=12x%5E2
x%5E4-12x%5E2%2B9=0 not factorable.

First solve for x^2 according to solution to quadratic formula;
x%5E2=%2812%2B-+sqrt%28144-4%2A9%29%29%2F%282%29
x%5E2=%2812%2B-+sqrt%28108%29%29%2F2
x%5E2=%2812%2B-+sqrt%284%2A9%2A3%29%29%2F2
x%5E2=6%2B-3%2Asqrt%283%29

and then
x=-(6-3*sqrt(3)) or x=(6-3*sqrt(3)) or x=-(6+3*sqrt(3)) or x=(6+3*sqrt(3))
'
FINAL ANSWER FOR JUST x: +x=-6%2B3%2Asqrt%283%29 or x=6-3%2Asqrt%283%29 or x=-6-3%2Asqrt%283%29 or x=6%2B3%2Asqrt%283%29