The product of five rational numbers is the following 10 numbers: - 12, 0.168, 0.2, 80, - 12.6, - 15, - 6000, 0.21, 84100. Please confirm these five rational numbers and briefly explain the reasons

The product of five rational numbers is the following 10 numbers: - 12, 0.168, 0.2, 80, - 12.6, - 15, - 6000, 0.21, 84100. Please confirm these five rational numbers and briefly explain the reasons

Arrange the pairwise products of five rational numbers from small to large: - 6000 ＜ - 15 ＜ - 12.6 ＜ - 12 ＜ 0.168 ＜ 0.2 ＜ 0.21 ＜ 80 ＜ 84 ＜ 100. ∵ there are four negative numbers and no 0 in the pairwise products of five rational numbers, or there are one negative number and four positive numbers, or one positive number and four negative numbers. (1) if the five rational numbers are one negative and four positive, it is better to set x1 ＜ 0 ＜ x2 ＜ x3 ＜ X4 ＜ X5, then x1x5 (where the size relationship between x2x5 and x3x4 can not be determined yet), the multiplication of (x1x4x5) 2 = 9 × 106, and ∵ X1 < 0, X4 > 0, X5 > 0, ∵ x1x4x5 = - 3000, then X1 = - 30, X4 = 0.5, X5 = 200. From x1 = - 30, x1x2 = - 12, x1x3 = - 12.6, then x2 = 0.4, X3 = 0.42 The test shows that X1 = - 30, X2 = 0.4, X3 = 0.42, X4 = 0.5, X5 = 200 satisfy the problem. (2) if these five rational numbers are 4 negative and 1 positive, it can be set as: X1 < x2 < X3 < X4 < 0 < X5, then x1x5 < x2x5 < x4x5 < 0 < x3x4x4x4 < x2x4x4 < x1x3 < x1x2, (where the size relationship between x1x4 and x2x3 can not be determined yet), then x1x5 = - 6000, x2x5 = - 15, x1x2 = 100, multiply the three formulas to get（ The solution is x1x2x5 = 3000, the solution is x1x2x5 = 3000, the solution is x1x2x5 = 3000, \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's not easy