Prove: A & # 178; + B & # 178; + C & # 178; ≥ AB + BC + AC

First of all, add that this inequality must be a > 1, b > 1, C > 1
The original equation is changed into:
a²+b²+c²-ab-bc-ac≥0
2a²+2b²+2c²-2ab-2bc-2ac≥0
(a-b)²+(b-c)²+(a-c)²≥0
And ∵ (a-b) & # 178; ≥ 0, (B-C) & # 178; ≥ 0, (A-C) & # 178; ≥ 0,
The original inequality holds
C studio answers for you,

RELATED INFORMATIONS

1. If a and B satisfy the absolute value of a + B-7 + (AB + Half) &# 178; = 0, find the value of 2 (a + b) + ab - (a + b) - 3AB
2. If x2 + X-1 = 0, then the value of the algebraic expression X3 + 2x2-7 is () A. 6B. 8C. -6D. -8
3. If AB is opposite to each other and CD is reciprocal to each other, then the algebraic formula (a + b) & # 178; - (CD) is 1 / 100
4. Given a = 2275, B = 2544, then the value of (a + b) 2 - (a-b) 2 is______ ．
5. Given that a, B and C are three sides of a triangle, is the value of the algebraic formula A & # 178; - 2Ab + B & # 178; - C & # 178; positive or negative, or 0?
6. [J, x ^ 2-3x-1 = 0, find the value of algebraic formula 1 / x ^ 2-2x-1 If possible, it can make me understand better
7. Given that x = 2 ^ M-1, y = 5 + 4 ^ m, we use the algebraic expression containing x to express y as
8. 2 (A & # 178; - AB) - 3 (2a & # 178; - AB) where a = - 2, B = 3, the evaluation is urgent!
9. Second grade mathematics (a ^ 2 + AB) / (a ^ 2 + 2Ab + B ^ 2), where a = - 3, B = 2, first reduce, then evaluate
10. Given that a + B = 32, ab = 1, the result of (A-2) (b-2) is () A. 1B. 2C. -1D. -2
11. Given a + B + C = 4, a & # 178; + B & # 178; + C & # 178; = 6, find AB + BC + AC =?
12. Calculation: (B-C) / (A & # 178; - AB AC + BC) - (C-A) / (B & # 178; - BC AB + AC) + (a-b) / (C & # 178; - AC BC + AB)
13. Calculation: (B-C) / (A & # 178; - AB AC + BC) - (C-A) / (B & # 178; - BC AB + AC) + (a-b) / (C & # 178; - AB BC + AB)
14. If A-B = 2, B-C = 1, then a & # 178; + B & # 178; + C & # 178; - AB BC AC= Hurry!
15. It is fast to find the indefinite integral Thank you Wrong. It's the power of the square of e ^ (- t)
16. In the indefinite integral of higher mathematics, is the order of u determined in the method of integration by parts against the power exponent three or against the power exponent three Please give an example to explain whether "three" can reach "Zhi", or "Zhi" can reach "three",
17. Given a = 2010, B = 2012, find quarter a & # 178; - half AB + quarter B & # 178;
18. Given that the quadratic function f (x) satisfies the conditions f (0) = 1, f (x + 1) - f (x) = 2x, the number of solutions of F (| x |) = a, a belonging to R is discussed
19. It is known that the quadratic function f (x) satisfies f (x + 1) - f (x) = 2x (x ∈ R), and f (0) = 1 It is known that f (x) is a quadratic function. For any x belonging to R, f (x + 1) - f (x) = - 2x + 1 and f (0) = 1 are satisfied (1) Finding the analytic expression of F (x) (2) When x belongs to [- 2,1], the image of y = f (x) is always above the image of F = - x + m, and the value range of real number m is obtained I would like to ask the following constant set up into a solution Is m ∈ [- 1,5] the answer? (2) In the question, f (x) = 2x + m has a solution, and the range of real number m is obtained
20. It is known that f (1-x) = f (1 + x) holds for any quadratic function f (x) belonging to R Let a = (SiNx, 2), B = (2sinx, 1 / 2), C = (cosx, 1), d = (1,2). When x belongs to [0, π], find the solution set of the inequality f (a × b) > F (C × d)