Find and prove the inequality that 1 / x + 1 / y is greater than or equal to 4 / x + y

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• 1. When x > 0, x > ln (1 + x)
• 2. Cauchy inequality solution: known a, B, C are positive numbers, prove: (A / B + B / C + C / a) (B / A + C / B + A / C) > = 9
• 3. The solution of the basic inequality y = (3 + X + X * x) / (1 + x) (x > 0) in high school mathematics
• 4. Given that x, y, Z are positive numbers and X + 2Y + 3Z = 2, then s = 1 / x + 2 / y + 3 / Z is the minimum
• 5. Given x + 2Y + 3x = 12, find the minimum value of x ^ 2 + 2Y ^ 2 + 3Z ^ 2
• 6. Given x + 2Y + 3Z = 12, find the minimum value of x ^ 2 + 2Y ^ 2 + 3Z ^ 2
• 7. If a, B, C, x, y, Z, > 0, X * 2 + y * 2 + Z * 2 = 1, find the minimum value of F (x, y, z) = A / x + B / y + C / Z
• 8. x. Y and Z are all positive numbers, and XYZ = 1. Prove that: (1 + X + y) (1 + y + Z) (1 + Z + Z) ≥ 27 Sorry, the letter is wrong, please verify: (1 + X + y) (1 + y + Z) (1 + Z + x) ≥ 27.
• 9. Given a (- 1, - 1), B (1,3), C (2,5), prove A.B.C three points collinear Fainting, forgetting that the line segment is obtained by subtracting
• 10. What is a six digit number with three fives and three zeros?
• 11. X + 4Y = 1 x y greater than 0 to find the minimum mean inequality process of 1 / x + 1 / Y
• 12. 1-2 / x + y = XY, 4Y + 6x = XY?
• 13. Given that two positive numbers x and y satisfy x + 4Y + 5 = XY, then the values of X and y are () A. 5，5B. 10，52C. 10，5D. 10，10
• 14. Positive integers x, y satisfy the equation x-4y = 78 and inequality 4 ≤ X-8 (Y-1) < 8, and find the value of XY
• 15. If x, y ∈ R + and X + 4Y = 1, then the maximum value of X · y is 0______ ．
• 16. Given | X-2 | + x ^ 2-xy + 1 / 4Y ^ 2 = 0, find the value of X and y
• 17. Who can help me to solve some simple basic inequalities and Cauchy inequalities Given (x ^ 2) + 2 (y ^ 2) = 1, find the maximum value of X + 2Y Given x + y + Z = 1, find the minimum value of 2 (x ^ 2) + 3 (y ^ 2) + Z ^ 2 A B C is a real number not less than 0 to prove a ^ 3 + B ^ 3 + C ^ 3 ≥ 3ABC If a and B satisfy AB = a + B + 3, the value range of AB can be obtained
• 18. Three dimensional Cauchy inequality a. B and C are positive numbers 1 1 1 1 1 1 — + — + — 》= ———+ —— + ——— 2a 2b 2c b+c c+a a+b 1/2a + 1/2b + 1/2c >= 1/(b+c) + 1/(c+a) + 1/(a+b)
• 19. On Cauchy inequality a. B are positive numbers, verification: B / A ^ 2 + A / b ^ 2 > 1 / A + 1 / b
• 20. The minimum positive period of the function y = 3sin ^ 2x + cos2x is? Such as the title