First read the following materials, and then answer the questions. Through observation, we find that the solution of the equation: x + 1 / x = 2 + 1 / 2 is X1 = 2, X2 = 1 / 2; X + 1 / x = 3 + 1 / 3 is X1 = 3, X2 = 1 / 3; X + 1 / x = 4 + 1 / 4 is X1 = 4, X2 = 1 / 4 Guess the solution of the equation X-1 / x = 1 and 1 / 2 about X and verify your conclusion

First read the following materials, and then answer the questions. Through observation, we find that the solution of the equation: x + 1 / x = 2 + 1 / 2 is X1 = 2, X2 = 1 / 2; X + 1 / x = 3 + 1 / 3 is X1 = 3, X2 = 1 / 3; X + 1 / x = 4 + 1 / 4 is X1 = 4, X2 = 1 / 4 Guess the solution of the equation X-1 / x = 1 and 1 / 2 about X and verify your conclusion

X-1 / x = 1 and 1 / 2 conjecture: x = 2, x = - 1 / 2 prove: X-1 / x = 1 and 1 / 2 (x ^ 2-1) / x = 3 / 22 (x ^ 2-1) = 3x2x ^ 2-2 = 3x2x ^ 2-3x-2 = 0 (X-2) (2x + 1) = 0, x = 2, x = - 1 / 2 prove the general formula X-1 / x = n and N / (n + 1) (x ^ 2-1) / x = [n (n + 1) + n] / (n + 1) (x ^ 2-1) / x = n (n + 2) / (n + 1) (x ^ 2-1)

First read the following materials, and then answer the question: the solution of the equation x + 1 / x = 2 + 1 / 2 is X1 = 2, X2 = 1 / 2; the solution of the equation x + 1 / x = 3 + 1 / 3 is X1 = 3, X2 = 1 / 3; the solution of the equation x + 1 / x = 2 + 1 / 2 is X1 = 2, X2 = 1 / 3;
In solving the equation: y + (y + 2) / y + 1 = 10 / 3, the transformation is x + 1 / x = a + 1 / A

Let X1 and X2 be the two roots of the equation 4x2-4mx + m + 2, and find the minimum value of X12 + X22

The discriminant is greater than or equal to 016m & sup2; - 16 (M + 2) > = 0m & sup2; - m-2 = (M + 1) (m-2) > = 0m = 2x1 + x2 = mx1x2 = (M + 2) / 4x1 & sup2; + x2 & sup2; = (x1 + x2) & sup2; - 2x1x2 = M & sup2; - 2 (M + 2) / 4 = (2m & sup2; - m-2) / 2 = [2 (m-1 / 4) & sup2; - 17 / 8] / 2m = 2, so m = - 1, minimum value