If the line y = x is the tangent of the curve y = x3-3x2 + ax, then a=______ ．

Let the tangent point P (x0, x0) ∵ the straight line y = x be the tangent of the curve y = x3-3x2 + ax ∵ the slope of the tangent is 1 ∵ y = x3-3x2 + ax ∵ y ′ x = x0 = 3x2-6x + a ∵ x = x0 = 3x02-6x0 + a = 1 ∵ the point P is on the curve ∵ x03-3x02 + ax0 = x0 ∵ from ① and ②, x0 = 03x20 − 6x0 + a − 1 = 0 ③ or X20 − 3x0

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1. If the line y = x is the tangent of the curve y = x3-3x2 + ax, then a=______ ．
2. RT tomorrow midterm exam this question is the original question, hope to have a concise answer Given that the curve C: y = x3-3x2 + 2x, the line L: y = KX, and the line L and the curve C are tangent to the point (x0, Y0) (x0 ≠ 0), the equation and tangent point coordinates of the line L are obtained
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6. If the line y = KX + 4 intersects the circle x ^ 2 + y ^ 2 = 1 or the curve y ^ 2 = x, then the value range of K is?
7. Given that hyperbola y = 3x and straight line y = KX + 2 intersect point a (x1, Y1) and point B (X2, Y2), and X12 + X22 = 10, find the value of K
8. The maximum range of objective function z = 3x + 2Y is [7,9], then the range of positive real number k is
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11. Given y = 2x + if the line y = KX + B is symmetric to the given line about the Y axis, find the values of K and B
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20. Solve the equation LNX = e + 1-x