Find and simplify the point(s) of intersection of the curves: x^2 + y^2 =6 , y = x - 3
Substituting y = x-3 into the first equation and expanding brackets:(x-3)2+x2 = 6 <=> 2x2 -6x +9 =6 <=> 2x2 -6x +3 =0Solving by using the quadratic formula:x=(6+- sqrt(36-4(2)(3)))/4 = (6+- sqrt(12))/4 Using the product rule for surds:x=(6+- 2sqrt(3))/4 = (3+- sqrt(3))/2Substituting back into y=x-3:y=(-3+- sqrt(3))/2So our final answer is: ( (3+sqrt(3))/2 , (-3+ sqrt(3))/2) and ( (3-sqrt(3))/2 , (-3- sqrt(3))/2)
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