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),
(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)=3*³√abc
RELATED INFORMATIONS
- 1. 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
- 2. 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 =?
- 3. 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 =?
- 4. 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=?
- 5. 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=______ .
- 6. 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 = ()
- 7. The difference between the reciprocal of two consecutive odd numbers is 2 / 143. What are the reciprocal of these two consecutive odd numbers?
- 8. 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,
- 9. The reciprocal difference between two consecutive odd numbers is 2 / 143. What are the two numbers?
- 10. The difference between the reciprocal of two consecutive odd numbers is 2 / 143. What is the reciprocal of these two consecutive odd numbers?
- 11. 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)
- 12. Let a and B be natural numbers and satisfy 11 / A + B / 3 = 17 / 33, then a + B = ()
- 13. Compare the fractions n / M and n-a / M-A (m, N, a, are all non-zero natural numbers)
- 14. 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,
- 15. M. N is a non-zero natural number, and 1 / M-1 / N = 2 / 143, M + n = () how to do
- 16. Natural numbers m, n satisfy m + n = 1991, prove: 10 ^ m + 10 ^ n is a multiple of 11? Who knows?
- 17. How many squares are there in natural numbers 100 to 200?
- 18. How to calculate the sum of incomplete squares of 100 natural numbers from 1 to 100?
- 19. 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=?
- 20. 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