Given that the real numbers a, B, C and D are not equal to each other, and a + 1b = B + 1C = C + 1D = D + 1A = x, try to find the value of X

Given that the real numbers a, B, C and D are not equal to each other, and a + 1b = B + 1C = C + 1D = D + 1A = x, try to find the value of X


From the known a + 1b = x, ①; B + 1C = x, ②; C + 1D = x, ③; D + 1A = x, ④; from the solution of ①, B = LX − a, ⑤ is substituted into ② to get C = x − AX2 − ax − 1, ⑥ is substituted into ③ to get x − AX2 − ax − 1 + 1D = x, that is DX3 - (AD + 1) X2 - (2d-a) x + AD + 1 = 0, ⑦ from ④ to get AD + 1 = ax, and substitute into ⑦ to get (D-A) (x