It is known that the parabola y = (k-1) x2 + 2kx + K-2 has two different intersections with the X axis (1) (2) when k is an integer and the solution of the equation 3x = kx-1 about X is negative, find the analytical formula of the parabola; (3) under the condition of (2), if you draw the largest square in the closed graph surrounded by the parabola and X axis, so that one side of the square is on the X axis and the two ends of the opposite side are on the parabola, try to find the largest square What's your side length?

It is known that the parabola y = (k-1) x2 + 2kx + K-2 has two different intersections with the X axis (1) (2) when k is an integer and the solution of the equation 3x = kx-1 about X is negative, find the analytical formula of the parabola; (3) under the condition of (2), if you draw the largest square in the closed graph surrounded by the parabola and X axis, so that one side of the square is on the X axis and the two ends of the opposite side are on the parabola, try to find the largest square What's your side length?

(1) According to the meaning of the title, we get that △ = 12K − 8 ＞ 0k − 1 ≠ 0, the value range of △ K is k ＞ 23 and K ≠ 1. ① (2) solve the equation 3x = kx-1, get x = − 13 − K, the solution of ∵ equation 3x = kx-1 is negative, and ∵ 3-K ＞ 0