If a and B are positive real numbers and a + 2B = 1, then the minimum value of 1A + 1b is 1______ .

If a and B are positive real numbers and a + 2B = 1, then the minimum value of 1A + 1b is 1______ .

∵ a + 2B = 1, ∵ 1A + 1b = (1a + 1b) (a + 2b) = 2 + AB + 2BA + 1 ∵ a, B is a positive real number, ∵ AB + 2BA ≥ 2, the minimum value of ab2ba = 22 + AB + 2BA + 1 ≥ 3 + 22 ∵ 1A + 1b is 3 + 22, so the answer is: 3 + 22
The quadratic power of 4x-6xy + 2x-3y and the quadratic power of AX + bxy + 3ax-2by
The sum of the quadratic power of 4x-6xy + 2x-3y and the quadratic power of AX + bxy + 3ax-2by does not contain the values of quadratic terms a and B
4X²-6XY+2X-3Y+aX²+bXY+3aX-2bY
=（4+a)x²+(b-6)xy+(3a+2)x-(2b+3)y
The formula does not contain quadratic term
4 + a = 0 and B-6 = 0
∴a=-4,b=6
Under the constraint condition: 2x + 5y10,2x-3y ≥ - 6,2x + y ≤ 10, the minimum value of Z = x2 + Y2 is obtained
Under the constraint conditions: 2x + 5Y ≥ 10,2x-3y ≥ - 6,2x + y ≤ 10, find the minimum value of Z = x2 + Y2
It's good to use analytic geometry. The part covered by 2x + 5Y ≥ 10 is the part above the line y = - 2 / 5x + 2, the part covered by 2x-3y ≥ - 6 is the part below the line y = 2 / 3x + 2, the part covered by 2x + y ≤ 10 is the part below the line y = - 2x + 10, and Z becomes the square of the distance from a certain point to the origin in this area
a. If B is a positive real number, then the minimum value of (2a + 1 / b) ^ 2 + (2B + 1 / a) ^ 2 is
RT
The original formula ≥ 2 "(2a + 1 / b) (2B + 1 / a)" square root
=Double radical (4AB + 4 + 1 / AB)
≥ 2 times root (4 + 2 times root 4AB * 1 / AB) = 4 times root 2
Because a and B are positive real numbers, so (2a + 1 / b) ^ 2 + (2B + 1 / a) ^ 2 is greater than or equal to 2 (2a + 1 / b) (2B + 1 / a) is equal to 8ab + 1 / AB + 8 is greater than or equal to 2 radical 8ab multiplied by 1 / AB and + 8 is equal to 4 radical 2 + 8.
So the minimum value is 4 root sign 2 + 8, if and only if AB = 1 / 2, the equal sign holds!
If the sum of the polynomials 4x-6xy + 2x-3y and ax + bxy + 3ax-2by of X and Y does not contain quadratic terms, the sum of the two polynomials is obtained
B-6 = 0, a + 4 = 0, a = - 4, B = 6 and: 2x-3y-12x-8y = - 10x-11y
It is known that real numbers x and y satisfy 2x + 5Y > = 10; 2x-3y > - 6; 2x + y
In this problem, we make the optimal domain of X and y, and find out the minimum value from the origin to the optimal domain. We know that the minimum distance is the distance from the origin to the straight line 2x + 5Y = 10, and the minimum value is the square of the minimum distance between the point and line, which is 100 / 29
If the real numbers a and B satisfy 2B * 2-A * 2 = 4, then the minimum value of | a-2b | is obtained
Please note: B and a are all squared, not multiplied by 2
If the sum of polynomials - axy2-12x and 14x-bxy2 is a monomial, then the relation between a and B is______ .
∵ the sum of the polynomials - axy2-12x and 14x-bxy2 is a monomial, ∵ - axy2-bxy2 = 0, that is - (a + b) XY2 = 0, the solution is a + B = 0. That is, a and B are opposite numbers to each other. So the answer is: opposite numbers to each other
Let m > 1, under the constraint condition {Y > = x, y
∵ m > 1, so the line y = MX intersects with the line x + y = 1 at (1 / (M + 1), M / (M + 1)), the line corresponding to the objective function z = x + my is perpendicular to the line y = MX, and the maximum value is obtained at (1 / (M + 1), M / (M + 1)), that is [(1 + m) / (M + 1)]
If real numbers a and B satisfy a + 2B = 2, find the minimum value of 2 ^ A + 2 ^ B
a+2b=2
2b=2-a
2^a+2^(2b)
=2^a+2^(2-a)
=2^a+2^(-a)*2^2>=2√[2^a*2^(-a)*2^2]=4
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