The proof of inequality (AC + BD) & sup2; ≤ (A & sup2; + B & sup2;) (C & sup2; + D & sup2;)

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• 1. It is proved that for any a, B, C and D, they belong to R, and there is an inequality (AC + BD) ^ 2
• 2. Prove the inequality: (A & sup2; + B & sup2;) (C & sup2; + D & sup2;) ≥ (AC + BD) & sup2;
• 3. It is proved that for any ABCD, there is always (AC + BD) & sup2; ≤ (A & sup2; + B & sup2;) (C & sup2; + D & sup2;)
• 4. It is proved that for any a, B, C, D ∈ R, there is an inequality (AC + BD) ≤ (a + b) (c + D),
• 5. Given C > 0, let P: function y = C ^ X be a decreasing function on R; Q: inequality x + | x-2c | >
• 6. On the existence of inequalities For any real number x, the inequality │ x + 1 │ + X-2 │ > a holds, and the value range of real number a is obtained Analysis 2: using the absolute value inequality │ a │ - B │ ＜ a ± B │ ＜ a │ + B │ to solve the minimum value of F (x) = │ x + 1 │ + X-2 │ Let f (x) = x + 1 + X-2, x + 1 + X-2 = 3, f (x) min = 3. A < 3 Why can we do this?
• 7. What's the difference between the solution of inequality and the existence of inequality? For example, is x greater than 1-B / a the same as x greater than 1-B / a? Good and quick answer,
• 8. In △ ABC, point D is the intersection of bisector of ∠ C and base ab. the following inequality is proved: CD & # 178; = AC · BC-AD · BD
• 9. Three inequalities are known: ① AB > 0. ② BC ad > 0. ③ C / a > D / b. taking two of them as conditions and the remaining one as conclusion, the number of correct propositions that can be formed is
• 10. If a > b, C
• 11. There are four inequalities: (1) A2 + B2 + C2 ≥ AB + BC + AC; (2) a (1-A) ≤ 14; (3) BA + ab ≥ 2; (4) (A2 + B2) (C2 + D2) ≥ (AC + BD) 2; where () A. 1 B. 2 C. 3 d. 4
• 12. Three inequalities are known: (1) AB > 0, (2) C / a > D / B, (3) BC > ad If two of them are taken as the conditions and the other one is taken as the conclusion, the composition can be formed______ A correct proposition
• 13. Three inequalities are known: (1) AB > 0; (2) C / a > - D / B; (3) BC > ad If two of them are taken as conditions and the remaining one as a conclusion, a correct proposition can be formed Wrong number~ Three inequalities are known: (1) AB > 0; (2) C / AAD
• 14. a. B, C, D are all real numbers. A group of values (a, B, C, d) which make the inequality AB > CD > 0 and ad < BC hold are______ (just write a set of values suitable for the condition)
• 15. If a, B, C and D are all real numbers, a set of inequalities (a, B, C, d) which make a / b > C / d > 0 and ad < BC hold are
• 16. If a, B, C and D are all real numbers, we try to list a set of values that make inequality a / b > C / d > 0 and ad > BC hold
• 17. Let a ^ n * (a ^ 2-B * c) + B ^ n (b ^ 2-ac) + C ^ n (C ^ 2-AB) > = 0 Prove a ^ n * (a ^ 2-B * c) + B ^ n (b ^ 2-ac) + C ^ n (C ^ 2-AB) > = 0, where n is any positive number
• 18. A, B and C are positive real numbers. Prove BC / A + AC / B + AB / C > = a + B + C
• 19. It is known that a, B and C belong to positive real numbers, and it is proved that (BC / a) + (AC / b) + (AB / C) > = a + B + C Second question: A + B + C = 1, proving: radical a + radical B + radical C
• 20. Factorization: A ^ 2 + 2Ab + 2ac-2bc-3b ^ 2