1. Verification: (1) A2 + B2 + 5 > = 2 (2a-b)
Compare the values of the following algebraic expressions (the first two are squares) A2 + B2 and 2A + 2b-2
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- 1. In the arithmetic sequence an, the first term A1 = 1, the sequence BN = (1 / 2) an, and B1. B2. B3 = 1 / 64, we prove A1B1 + a2b2 +... + anbn
- 2. Anbn... A2N = A1B1 c1d1.. where all elements not written out are zero... CN DN calculate its determinant an bn .. .. .. A2n = a1b1 c1d1 ... where the unwritten elements are zero .. .. cn dn Calculate its determinant The prototype of the title probably knows that the title is a bit misplaced
- 3. For X ∈ R, the inequality | 2-x | + | 1 + X | ≥ a2-2a holds, then the value range of real number a is______ .
- 4. For any x ∈ R, if the inequality AX2 - | x + 1 | + 2A ≥ 0 holds, then the value range of real number a is______ .
- 5. a. B, C ∈ r a + B + C = 1 to prove ((1 / a) - 1) ((1 / b) - 1) ((1 / C) - 1) ≥ 8
- 6. Given the points a (5,1,3), B (1,6,2), C (5,0,4), D (4,0,6), find a normal vector of a, B and plane parallel to CD
- 7. 8 1 / 5-3 3 / 10 + 1 4 / 15
- 8. It is known that a, B, C and D satisfy a + B = 1, C + D = 1, AC + BD > 1
- 9. Given three points, a (- 1, - 1) B (3,3) C (4,5): three points collinear
- 10. It is known that a, B, C. belong to R +, and a + B + C = 1, and 1 / A + 1 / B + 1 / C > = 9 is proved
- 11. Arrange the 100 numbers of 1, 2, 3, 4, 5, 6, 100 randomly as A1, A2, A3, A4, A5, if the adjacent two Put 1,2,3,4,5 The 100 numbers of 100 are arranged arbitrarily as A1, A2, A3, A4, A5 A100. If two adjacent numbers on the left are larger than those on the right, exchanging their positions is called one exchange. Until the 100 numbers on the left are larger than those on the right, now we know that the fourth number is 40, and the 95th number is 99. How many exchanges should we arrange this group of numbers at most Yes, come and no, go away. The answer is 4800. What I want is the process
- 12. If R (B1, B2, B3)
- 13. (B1, B2. B3) = (A1, A2, A3) * an invertible matrix. Why is B1, B2, B3 linearly correlated?
- 14. A1 + a3 + A5 + A7 = 4, find A2 + A4 + A6
- 15. In the positive proportional sequence {an}, A4 + a3-a2-a1 = 5, then the minimum value of A5 + A6 is______ .
- 16. Eight year mathematics A2 + B2 = √ 13, A-B = 1, find A3 + B3
- 17. A set of formulas arranged in regular order: - B2 / A, B5 / A3, - B8 / A3, B11 / A4... (AB is not equal to 0) find the seventh formula and the nth formula. (n is a positive integer)
- 18. If vector group A1, A2, A3 are linearly independent, it is proved that vector group B = a1 + 2A2, B2 = A2 + 2A3, B3 = A3 + 2A1 are linearly independent
- 19. Linear algebra problem: find a unit vector in R ^ 4 so that it is orthogonal to the following three vectors: A1 (1,1, - 1,1), A2 (1, - 1, - 1,1), A3 (2,1,1,3) Request solution process, please help me
- 20. Given a vector (A1, A2, A3) and B vector (B1, B2, B3), then A1 / B1 = A2 / B2 = A3 / B3 is a sufficient condition of a vector / / b vector If a vector (A1, A2, A3) and B vector (B1, B2, B3) are known, then A1 / B1 = A2 / B2 = A3 / B3 is a sufficient and unnecessary B necessary C sufficient and necessary D of a vector / / b vector