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______ .
For the equation x2-ax + 34b2 = 0 of X has real roots, then the discriminant △ = A2-4 × 34b2 = a2-3b2 ≥ 0, that is, (a-3b) (a + 3b) ≥ 0, make the plane region corresponding to the inequality system as shown in the figure: then the slope of a-3b = 0 is k = 33, the corresponding inclination angle is 30 °, the slope of a + 3B = 0 is k = - 33, the corresponding inclination angle is 150 °
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- 1. 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
- 2. 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
- 3. The real solution of the equation (2 + I) x square minus (5 + I) x plus (2 minus 2I) = 0 is
- 4. 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
- 5. Proof: the equation AX ^ 2 + 2x + 1 = 0 of X has at least one negative root if and only if a
- 6. 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
- 7. 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
- 8. Inequality ax ^ 2 + ax + A-1 I think we should discuss the scope of X
- 9. 1. If the univariate quadratic equation x2 + ax + 1 ≥ 0 holds for all real numbers x, find the value range of real number A. (what is △ at this time?) For all real numbers x, the inequality AX2 + 4x + a > 1-2x2 holds, and the value range of real number a is obtained Ask specific process.. the teacher did not speak carefully And when △ why is constant established? Is constant meaningful?
- 10. Given that the equation AX ^ 2 + BX-1 = 0 (AB belongs to R and a > 0) has two real roots, one of which is in the interval (1,2), what is the value range of A-B The answer is (- 1, positive infinity). I want a simple and understandable solution
- 11. 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______ .
- 12. 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___ .
- 13. 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
- 14. Decomposition factor: (AX by) cubic + (by CZ) cubic - (AX CZ) cubic
- 15. 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
- 16. 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
- 17. 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
- 18. 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?
- 19. 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
- 20. 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?