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a. B, C belong to R+ Verification: A ^ 2 / (B + C) + B ^ 2 / (a + C) + C ^ 2 / (a + b) > = (a + B + C) / 2
This paper first introduces the important Cauchy Inequality: (A1 & sup2; + B1 & sup2; + C1 & sup2;) (A2 & sup2; + B2 & sup2; + C2 & sup2;) > = (A1A2 + b1b2 + C1C2) & sup2; expressed in words: square sum product > = product sum square [A & sup2; / (B + C)] + B & sup2; / (a + C) + C & sup2; / (a + b)] ((B + C) + (a + C) + (a + b)) ≥ (a +
RELATED INFORMATIONS
- 1. Let x ^ 2 + (Y-1) ^ 2 ≤ 4, find the maximum value of (x + Y-1) / (X-Y + 3)
- 2. 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
- 3. 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)
- 4. |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
- 5. 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
- 6. 2.4 × 105 36.79 × 99 + 36.79 simple calculation
- 7. What do numbers in pairs mean?
- 8. What does number pair (3,5) mean
- 9. What are the meanings of the two numbers in the number pair?
- 10. -The meaning of each number of (+ 2) - (2.7) - (- 3)
- 11. 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
- 12. It is known that a ＞ B ＞ C, and verified that 1a − B + 1b − C ≥ 4A − C
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. 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
- 18. In triangle ABC, angle a = 3, angle B, angle a-angle C = 30 degrees, then angle a =? Angle B =? Angle c =?
- 19. 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
- 20. In △ ABC, a = 45 °, C = 30 ° and C = 10cm, find a, B and B