The mean inequality problem, It is known that ABCD > A ^ 2 + B ^ 2 + C ^ 2 + D ^ 2, ABCD is a real number

∵a²+b²+c²+d² ≥ 2ab+2cd ≥ -(a²+b²+c²+d²),∴(a²+b²+c²+d²)² ≥ (2ab+2cd)² = 4a²b²+4c²d²+8abcd ≥ 16abcd.∵abcd...

RELATED INFORMATIONS

1. Let a, B and C be positive real numbers, and prove that 12a + 12b + 12C ≥ 1b + C + 1C + A + 1A + B
2. The question of mean inequality X + y + Z = Pi, find the maximum value of SiNx + siny + Sinz The sum difference product is (3 / 2) * radical 2, but if we use the mean inequality, SiNx + siny + Sinz > = 3 (sinxsinysinz) ^ (1 / 3). When x = y = z = pi / 3, we take equality, and the minimum value is (3 / 2) * radical 2. What's the matter? 0
3. A and B leave each other from two places 360 km away. It is known that the speed of a is 60 km / h and that of B is 40 km / h. If a leaves for one hour first, how long will it take for B to meet each other?
4. A plane flies between two cities, The wind speed is 24 km / h, it takes 2 hours and 50 minutes to follow the wind. It takes 3 hours to fly against the wind. To find the distance between the two cities and the speed of the aircraft itself, we need to use the one member first-order equation!
5. The goods can be transported 6 / 5 in 6 days by ab. if the goods are transported alone, it takes the same time for a to transport 3 / 1 and B to transport 2 / 1
6. A batch of saplings were transported to afforest the campus. 82 saplings were transported for the first time and 78 saplings were transported for the second time. Four fifths of the total saplings were transported for the second time. How many saplings are there in total
7. There are 60 male workers in the first workshop. Male workers are one third of female workers. How many female workers are there?
8. The awareness of the school chorus is more than three times that of the dance team There were () students in the chorus Only the chorus!
9. A total of 13 boys and girls went to the park to plant trees. Each boy planted 6 trees, and each girl planted 4 trees. A total of 64 trees were planted. How many boys and girls were there? You can't use equations! Help!
10. When a, B and C go shopping together, 1 / 2 of a's spending is equal to 1 / 3 of B's spending, and 3 / 4 of B's spending is equal to 3 / 5 of C's spending Spend 98 yuan more than a, ask them how much money they spend in total? Not three yuan equation, we primary school students, ask for help
11. The minimum value of the X + 1 power of y = 2 + the - x power of 2 is? (using mean inequality)
12. Find the maximum value of F (x), using the mean inequality! Let x > - 1, find the inequality of the maximum mean value of F (x) = (x + 5) * (x + 2) / (x + 1)~ And the maximum~~~~
13. Using the mean inequality method to find the range and the maximum value: y = x ^ 2 × (3-2x)
14. Mean inequality when 0
15. Given that X and y are greater than zero. 1 / x + 2 / y + 1 = 2, then the minimum value of 2x + y is the mean inequality,
16. The range of y = x + x-3 / 1 (x is greater than 3) is determined by means inequality method
17. FX = x (1-x & # 178;) for fixed value (mean inequality)
18. Prove 1-p (a ~) - P (b ~)
19. A proof of inequality Given that a, B and C are positive real numbers and ab + BC + Ca = 3, it is proved that a ^ 2 + B ^ 2 + C ^ 3 + 3ABC ≥ 6 That's right!
20. Algebraic inequality 1 Let x, y, Z ∈ R +, prove: X √ [x / (1 + YZ)] + y √ [y / (1 + ZX)] + Z √ [Z / (1 + XY)] ≥ 3 / √ (1 + XYZ)