It is known that a > B > C, and verified that 1a − B + 1b − C ≥ 4A − C
It is proved that: ∵ a − Ca − B + a − CB − C = a − B + B − Ca − B + a − B + B − CB − C = 2 + B − Ca − B + a − BB − C ≥ 2 + 2B − Ca − B × a − BB − C = 4, (a > B > C) ∵ a − Ca − B + a − CB − C ≥ 4 ∵ 1a − B + 1b − C ≥ 4A − C
RELATED INFORMATIONS
- 1. Proving inequality The existing one component sequence is (1 / 10) ^ 2 + (1 / 11) ^ 2 + (1 / 12) ^ 2 + +(1/1000)^2 Try to prove that the sequence is greater than 0.099 and less than 0.111
- 2. a. B, C belong to R+ Verification: A ^ 2 / (B + C) + B ^ 2 / (a + C) + C ^ 2 / (a + b) > = (a + B + C) / 2
- 3. Let x ^ 2 + (Y-1) ^ 2 ≤ 4, find the maximum value of (x + Y-1) / (X-Y + 3)
- 4. An inequality problem in Senior High School~~ 10. It is known that P > 0, Q > 0, the median of p q is 1 / 2, and x = P + 1 / P, y = q + 1 / Q, then the minimum value of X + y is () A.6 B.5 C.4 D.3
- 5. It is known that a, B and C are the three sides of a triangle, Verification: C / (a + b) + A / (B + C) + B / (c + a)
- 6. |x+1|≤a |x-2|≤a Above is a system of inequalities, and a is less than 0 Sorry ~ A is greater than 0! Sorry
- 7. Define a new operation with "[": for any rational number a, B has a [b = B ^ 2 + 1, for example, 7 [4-4 2+1=17. 1. Fill in the blanks: 5 [=_____ ; 2. When m is a rational number, find the value of M [, (2) Given that m and N are opposite numbers, X and y are reciprocal numbers, | a | = 1, try to find the value of a ^ 2 - (M + n) ^ 2012 + (- XY) ^ 2012 Define a new operation with "[": for any rational number a, B has a [b = B ^ 2 + 1, for example, 7 [4-4 ^ 2 + 1 = 17
- 8. 2.4 × 105 36.79 × 99 + 36.79 simple calculation
- 9. What do numbers in pairs mean?
- 10. What does number pair (3,5) mean
- 11. A proof of inequality in Senior High School Let x, y, Z satisfy x + y + Z = 1 Verification: x ^ 2 / (y + 2Z) + y ^ 2 / (Z + 2x) + Z ^ 2 / (x + 2Y) > = 1 / 3
- 12. A problem of basic inequality in Senior High School If the positive numbers x and y satisfy 2x + 3Y = 11 / x + 1 / y, the minimum value is
- 13. For any real numbers a (a ≠ 0) and B, the inequality | a + B | + | A-B | ≥ m · | a | holds. Note that the maximum value of real number m is m. (1) find the value of M; (2) solve the inequality | X-1 | + | X-2 | ≤ M
- 14. Given 1 > a > b > C > 0, we prove that (1-A) · (1-B) · (1-C) is greater than or equal to 8abc It is known that the three sides of a triangle with perimeter 1 are A.B., C
- 15. Trinomial inequality a + B + C ≥ how many a & # 178; + B & # 178; + C & # 178; greater than or equal to how many a ^ 3 + B ^ 3 + C ^ 3 ≥ how many
- 16. In triangle ABC, angle a = 3, angle B, angle a-angle C = 30 degrees, then angle a =? Angle B =? Angle c =?
- 17. As shown in the figure, in △ ABC, the vertical bisector of AB intersects at D, de = 6, BD = 62, AE ⊥ BC at e, and the length of EC is obtained
- 18. In △ ABC, a = 45 °, C = 30 ° and C = 10cm, find a, B and B
- 19. It is known that, as shown in the figure, in △ ABC, ad and AE are the bisectors of height and angle of △ ABC respectively, if ∠ B = 30 ° and ∠ C = 50 ° (1) find the degree of ∠ DAE; (2) try to write out the relationship between ∠ DAE and ∠ C - ∠ B? (no proof required)
- 20. The product of a number multiplied by a true fraction must be less than this number______ (judge right or wrong)