If x, y ∈ R + and X + 4Y = 1, then the maximum value of X · y is 0______ .
Xy = 14x · 4Y ≤ 14 (x + 4y2) 2 = 116, if and only if x = 4Y = 12, take the equal sign
RELATED INFORMATIONS
- 1. Positive integers x, y satisfy the equation x-4y = 78 and inequality 4 ≤ X-8 (Y-1) < 8, and find the value of XY
- 2. 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
- 3. 1-2 / x + y = XY, 4Y + 6x = XY?
- 4. X + 4Y = 1 x y greater than 0 to find the minimum mean inequality process of 1 / x + 1 / Y
- 5. Find and prove the inequality that 1 / x + 1 / y is greater than or equal to 4 / x + y
- 6. When x > 0, x > ln (1 + x)
- 7. Cauchy inequality solution: known a, B, C are positive numbers, prove: (A / B + B / C + C / a) (B / A + C / B + A / C) > = 9
- 8. The solution of the basic inequality y = (3 + X + X * x) / (1 + x) (x > 0) in high school mathematics
- 9. Given that x, y, Z are positive numbers and X + 2Y + 3Z = 2, then s = 1 / x + 2 / y + 3 / Z is the minimum
- 10. Given x + 2Y + 3x = 12, find the minimum value of x ^ 2 + 2Y ^ 2 + 3Z ^ 2
- 11. Given | X-2 | + x ^ 2-xy + 1 / 4Y ^ 2 = 0, find the value of X and y
- 12. 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
- 13. 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)
- 14. On Cauchy inequality a. B are positive numbers, verification: B / A ^ 2 + A / b ^ 2 > 1 / A + 1 / b
- 15. The minimum positive period of the function y = 3sin ^ 2x + cos2x is? Such as the title
- 16. When x ∈ (0, π), the minimum value of F (x) = 1 + cos2x + 3sin2xsinx is () A. 22B. 3C. 23D. 4
- 17. It is proved that 1 + sin2 θ + Cos2 θ / 1 + sin θ - Cos2 θ = Tan θ
- 18. How does cos square become 1 / 1 + Tan square theta
- 19. (Tan x + cot x) cos square x=
- 20. Square of sin β + square of cos β + Tan β cot β