If any two real numbers a and B are taken in the interval [- 2,2], then the probability of two real numbers of X equation x ^ 2 + ax-b ^ 2 + 1 = 0? The equation is: x ^ 2 + 2ax-b ^ 2 + 1 = 0

π/2
Delta = a ^ 2 + 4B ^ 2-4 > 0, it is an ellipse, the major and minor axes are 2 and 1 respectively, the area is 2 π, and it is completely in the square of [- 2,2] ^ 2, the area is 4,
SO 2 π / 4 = π / 2

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1. In the interval [- 1,1], take any two points a and B, and the probability that the two points of equation x2 + ax + B = 0 are both real numbers is p, then the value range of P is___ ．
2. If the real numbers a and B satisfy A2 + B2 ≤ 1, then the probability of the equation x2-ax + 34b2 = 0 with real roots is zero______ ．
3. If the real numbers a and B satisfy A2 + B2 ≤ 1, then the probability of the equation x2-ax + 34b2 = 0 with real roots is zero______ ．
4. F (x) = ax + BX + 1 (a, B ∈ R) if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression of F (x) is obtained F (x) = ax + BX + 1 (a, B ∈ R) ① if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression for finding f (x) holds. ② under the condition of ①, when x ∈ [- 2,2], G (x) = f (x) - KX is a monotone increasing function, the value range of real number k can be found
5. The equation | x ^ 2 + ax + B | = 2 of X has three different real numbers, and the three different real numbers are exactly three sides of a right triangle. Find the right triangle
6. The real solution of the equation (2 + I) x square minus (5 + I) x plus (2 minus 2I) = 0 is
7. p: For any real number x, KX square plus 2, KX minus (k plus 2) is less than 0. Q: for the equation x of X, the square plus x minus K is equal to 0, and there is a real root if P and Q p: For any real number x, KX square plus 2, KX minus (k plus 2) is less than 0. Q: for the equation x of X, the square plus x minus K is equal to 0. There is a real root. If there is only one true proposition between P and Q, the value range of the real number k is determined
8. Proof: the equation AX ^ 2 + 2x + 1 = 0 of X has at least one negative root if and only if a
9. Let a = {(x, y) | y = 2x-1, X ∈ positive natural number}, B = {(x, y) | y = ax ^ 2-ax + A, X ∈ positive natural number}, ask whether there is a non-zero real number a, let a ∩ B be If there is a single element set, find out the value of A. if not, explain the reason
10. Let a = {(x, y) | y = 2x-1, X ∈ n *}, B = {(x, y) | y = AX2 ax + A, X ∈ n *}, ask whether there is a non-zero integer a, so that a ∩ B ≠? If it exists, request the value of a; if it does not exist, explain the reason
11. Decomposition factor: (AX by) cubic + (by CZ) cubic - (AX CZ) cubic
12. If the degree of cube + 2x Square-1 of polynomial ax is the same as that of 2x-3xb, what conditions should a and B satisfy
13. It is known that ax + by = 7, ax's square + by's Square = 49, ax's cube + by's cube = 133, ax's fourth power + by's fourth power = 406 Find the value of 17 (a + b) of 1999 (x + y) + 6xy-2
14. To solve the system of equations ax + by = 16 BX + ay = 19, Xiaoming gets x = 1y = 7 and Xiaoliang gets x = - 2Y = 4. To solve the system of equations ax + by = 16 BX + ay = 19, Xiaoming gets x = 1y = 7 and Xiaoliang gets x = - 2Y = 4, how about finding the correct solution and the original equation? As of 10 o'clock, speed answer
15. Xiao Ming and Xiao Liang solve the same system of equations (1) ax + by = 1 (2) BX + ay = - 5. Xiao Ming miscopies (1) and gets the solution as x = - 1, y = 3; while Xiao Liang miscopies (2) and gets the solution as x = 3, y = 2. Can you correctly find the solution of the original system of equations according to the above results?
16. In the system of equations ax + by = 16 1 BX + ay = 19 2, copy 1 wrong to x = 1 y = 1, Xiao Liang copy 2 wrong to x = - 2 y = 4 to find the correct answer 16 and 1 are separated, 1 with a table, 19 and 2 are also not good oral expression
17. When solving the equations {ax + by = 16 ① BX + ay = 19 ②, Xiao Ming copied the equation ① wrong and got the wrong solution {x = 1, y = 7), while Xiao Liang copied the equation ② wrong What is the original system of equations?
18. If the solution of the system of equations ax-by-2z = 13 ax + 2Y + CZ = - 2 about X, y and Z is x = 3, y = - 1, z = - 2, cx-4y + BZ = 31, the value adding process of a, B and C is obtained
19. Take any point P in the interior or boundary of △ ABC, and note that the distances from P to three sides a, B, C are x, y, Z in turn. Prove that ax + by + CZ is a constant
20. The solution of the system ax + by = 2C CZ + AX = 2B by + CZ = 2A is a. B and C are constant and not 0