+1859 What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates are in increasing order. (So "(1,-3), (2,3), (5,-7)" - without the quotes - is a valid answer format.)
+129771 x^3 + x^2 -3x + 5 = x^3 + 2x^2
x^2 + 3x - 5 = 0
x^2 + 3x = 5 complete the square on x
x^2 + 3x + 9/4 = 5 + 9/4
(x + 3/2)^2 = 29/4 take both roots
x + 3/2 = sqrt (29/4) x + (3/2) = -sqrt (29/4)
x = [sqrt (29 - 3 ] / 2 x = [ -sqrt (29) - 3 ] / 2
y = [-sqrt (29) - 3 ] / 2 y = [sqrt (29) -3 ] / 2
(x,y) = ( [sqrt (29 -3 ] /2 , [-sqrt (29)-3 ] /2 , [-sqrt (29) -3 ] / 2 , [ sqrt (29) - 3 ] / 2 )
