If two of the equations lg2x + (lg5 + lg7) lgx + lg5 · lg7 = 0 are α and β, then the value of α · β is ()

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• 1. If the two roots of the equation lg2x + (lg5 + lg7) lgx + lg5lg7 = 0 are X1 and X2, then X1 * x2 =?
• 2. Please help me to analyze my doubts in the following problems, exercise: the equation lg2x / LG (x + a) = 2, ask why a is worth, the equation has a solution? arrangement: lg2x=2lg(x+a) 2x=(x+a)^2 The results are as follows x^2+2(a-1)x+a^2=0 And 2x > 0, x + a > 0, For the above univariate quadratic equation, △ = 4 [(A-1) ^ 2] - 4 (a ^ 2) = - 8A + 4, There are three cases ① When △ 0, - 8A + 4 > 0, a < 1 / 2 In this case, the equation has two solutions, X = {2-2a ± [radical (4-8a)} / 2 = 1-A ± [radical (1-2a)] In this case, x = (1-A) + [radical (1-2a)] > 0 is obviously true (positive number plus positive number); For x = (1-A) - [radical (1-2a)], since (1-A) ^ 2 - (1-2a) = 1-2a + A ^ 2-1 + 2A = a ^ 2 > 0, x = 1-A - [radical (1-2a)] > 0 also holds However, because x + a > 0 is required, Therefore, when a ＜ 1 / 2 and X + a ＞ 0, the original equation has two solutions ② When △ = 0, a = 1 / 2 In this case, the equation is x ^ 2-x + 1 / 4 = 0, and the unique solution is x = 1 / 2 But it is meaningless that the denominator is 0 Therefore, when x = 1 / 2, the original equation has no solution ③ When △ 0, a ＞ 1 / 2, the original equation has no solution To sum up, (1) When a < 1 / 2, the equation has two solutions; (2) There is no a such that the equation has a solution; (3) When a ≥ 1 / 2, the equation has no solution My question is: 1, "for x = (1-A) - [root (1-2a)], since (1-A) ^ 2 - (1-2a) = 1-2a + A ^ 2-1 + 2A = a ^ 2 > 0", how can I get 1-A - √ (1-2a) > 0 from this? 2. "When a ＜ 1 / 2 and X + a ＞ 0, the original equation has two solutions." why? From 2x > 0, we can get x > 0; X + a > 0, we can get x > - A. why not find the maximum value of - x, and then combine A0 and 2x > 0, that is, x > 0 and x > - A. should we also find the maximum value of - x, and then find the range of a? Even if we can't find it, should we also meet a > - x? Why only a > 2
• 3. A particle moves in the first vector of oxy in the plane coordinate system. The trajectory equation is xy = 16, and the change rule of X with time t is x = 4T ^ 2 (t is not equal to 0). The velocity of the particle at t = 1s can be calculated by taking X and Y as M
• 4. A particle moves in the XY plane, the equation of motion is x = 3T, y = 2T ^ 2 + 3, where t is calculated as s, x, y is calculated as m, and the solution is obtained in the period of T = 1s and T = 2S Find the size and direction of the displacement of the particle in this period of time
• 5. The equation of motion of a point moving in the xoy plane is x = 2T, y = 19-2t ^ 2. When is the vector of the particle perpendicular to the velocity?
• 6. Known particle kinematics equation is x = (10 + 3T ^ 2) I + 2T ^ 2J, help me find its trajectory equation; thank you
• 7. There is a moving particle in the oxy plane, and the de motion function is r = 3Ti + 10 ^ 2J (SI) With an explanation
• 8. If the motion equation of a particle in oxy plane is r = (4sin2 π T) I + (4cos2 π T) J, then the trajectory equation of the particle is?
• 9. The motion equation of a particle moving in the oxy plane is r = 2Ti + (19-2t) J (SI system). Find: (1) the trajectory equation of the particle, (2) the position, velocity and acceleration of the object when T1 = 2S, (3) the average velocity from T1 = 2S to T2 = 3S
• 10. How to factorize x ^ 3 + 2x ^ 2 + 1 = 0
• 11. It is proved that the quadratic equation x 2 + (a + 1) x + 2 (A-2) = 0 must have two unequal real roots
• 12. Solving the fourth order determinant! A 100 - 1 B 100 - 1 C 100 - 1 D Four in a row~
• 13. It is known that the quadratic equation (ab-2b) x & # 178; + 2 (B-A) x + 2A AB = 0 has two equal real roots, then the real roots are A-1 B1 C0 D-2
• 14. Let f (x) satisfy AF (x) + BF (1-x) = C / x, a, B and C are constants, and the absolute values a and B are unequal, then f (x) is obtained
• 15. The maximum value of function f (x) = 2x ^ 3-2x ^ on [- 1,2]
• 16. What is the maximum m (a) of the quadratic function f (x) = - 2x Λ 2-8ax + 3 (0 ≤ x ≤ 4)
• 17. Let f (x) = 2x + 3, G (x + 3) = f (x), find the expression of G (x), please tell me quickly, thank you
• 18. Given the function f (2x-3) = 2x-1, find the expression of function f (x)
• 19. Given the function f (x) = a ^ x + B (a > 0, and a ≠ 1), f (0) = 2, f (1) = 3, the analytic expression of the function is f (x)=
• 20. If the function f (x) = 4x ^ 2-kx-8 is not monotone in the interval [5,20], then the value range of real number k is