The line 5x 5y = 2 intersects the curve x 2 y 5x + y

Question:

The line 5x – 5y = 2 intersects the curve x2y – 5x + y + 2 = 0 at three points.

a. Find the coordinates of the points of intersection.

b. Find the gradient of the curve at each of the points of intersection.

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