Let a, B, C be real numbers, and prove: A & sup2; B & sup2; + B & sup2; C & sup2; + A & sup2; C & sup2; ≥ ABC (a + B + C)

It is proved that: ∵ A & sup2; B & sup2; + B & sup2; C & sup2; ≥ 2Ab & sup2; C,
b²c²+c²a²≥2abc²,
c²a²+a²b²≥2a²bc,
The above three inequalities add up to a & sup2; B & sup2; + B & sup2; C & sup2; + C & sup2; a & sup2; ≥ ABC (a + B + C)

RELATED INFORMATIONS

1. It is proved that √ A & sup2; + B & sup2; + C & sup2; / 3 ≥ a + B + C / 3 ≥ & sup3; √ ABC (where a, B, C ∈ positive real numbers, and each pair is unequal),
2. Step 1: take a natural number N1 = 5, calculate the square of N1 plus 1 to get A1; step 2: calculate the sum of all numbers of A1 to get N2, calculate the square of N2 plus 1 to get A2 Three steps: calculate the sum of the numbers of A2 to get N3, and add 1 to the square of N3 to get A3
3. The first step: take a natural number N1 = 5, calculate N1 + 1 to get A1; the second step: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· V step 1: take a natural number N1 = 5, calculate the square of N1 + 1 to get A1; step 2: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· Step 3: calculate the sum of the numbers of A2 to get N3, and then calculate the square of N2 The first step: take a natural number N1 = 5, calculate the square of N1 + 1 to get A1; the second step: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· Step 3: calculate the sum of the numbers of A2 to get N3, and then calculate the square of N2 to get A3... And so on, then A2010 =?
4. The first step is to take a natural number N1 = 5 and calculate the square 1 + 1 of n to get A1; the second step is to calculate the sum of the digits of A1 to get N2 and calculate the square 2 + 1 of n to get A2; Step 3: calculate the sum of the digits of A2 to get N3, and calculate the square 3 + 1 of n to get A3; '; then A2010 =?
5. The first step: take a natural number N1 = 5, calculate the square of N1 + 1 to get A1; the second step: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2 Step 3: calculate N3 of the sum of the numbers of A2, and then calculate the square of N3 to get A3 a2011=?
6. Step 1: take a natural number N1 = 5, calculate the square of N1 + 1 = A1. Step 2: calculate the sum of all the numbers of A1 to get N2, The first step: take a natural number N1 = 5, calculate N1 square + 1 = A1 Step 2: calculate the sum of the numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2 Step 3: calculate the sum of the numbers of A2 to get N3, and calculate N3 square + 1 to get A3 …… And so on, A2012=______ .
7. 3、 Step 1: take a natural number N1 = 5, calculate the quadratic power + 1 of N1 to get α 1; step 2: calculate the sum of the numbers of α 1 to get N2, calculate the quadratic power + 1 of N2 to get α 2; step 3: calculate the sum of the numbers of α 2 to get N3, and then calculate the quadratic power + 1 of N3 to get α 3 By analogy, α 2011 = ()
8. The difference between the reciprocal of two consecutive odd numbers is 2 / 143. What are the reciprocal of these two consecutive odd numbers?
9. The difference between the reciprocal of two consecutive odd numbers is 2 / 143. What are the reciprocal of these two consecutive odd numbers To explain,
10. The reciprocal difference between two consecutive odd numbers is 2 / 143. What are the two numbers?
11. Let a and B be natural numbers and satisfy 11 / A + B / 3 = 17 / 33, then a + B = ()
12. Compare the fractions n / M and n-a / M-A (m, N, a, are all non-zero natural numbers)
13. If the natural number AB satisfies 1 / A-1 / b = 1 / 182 and a: B = 7:13, what is the sum of a + B Why is this 13 / 7b-1 / b = 1 / 182 Here is (13-7) / 7b = 1 / 182 Why (13-7) / 7b = 1 / 182 The process should be very detailed,
14. M. N is a non-zero natural number, and 1 / M-1 / N = 2 / 143, M + n = () how to do
15. Natural numbers m, n satisfy m + n = 1991, prove: 10 ^ m + 10 ^ n is a multiple of 11? Who knows?
16. How many squares are there in natural numbers 100 to 200?
17. How to calculate the sum of incomplete squares of 100 natural numbers from 1 to 100?
18. For the natural number n, the sum of the numbers is Sn, such as s2005 = 2 + 0 + 0 + 5 = 7, then S0 + S1 + S2004+S2005=?
19. The sum of all digits of natural number n is Sn, such as n = 38, Sn = 3 + 8 = 11; n = 247, Sn = 2 + 4 + 7 = 13. If n-sn = 2007 is satisfied for some natural numbers, the maximum value of n is () A. 2025B. 2023C. 2021D. 2019
20. Let a = {x | x = 2n + 1, n ∈ n}, B = {x | 1 ≤ x ≤ 10}, C = {x | x = 3N, n ∈ n}, find (a ∩ b) ∩ C