Given 4x ^ + 9y ^ 2-4x + 12Y + 5 = 0, find the value of X + y

Given 4x ^ + 9y ^ 2-4x + 12Y + 5 = 0, find the value of X + y

4X^+9Y^2-4X+12Y+5=0
（4x²-4x+1）+(9y²+12y+4)=0
(2x-1)²+(3y+2)²=0
x=1/2 y=-2/3
xy=1/2-2/3=-1/6
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In rectangular coordinate system, if the curve represented by equation m (x ^ 2 + y ^ 2 + 1) = (x-2y + 3) ^ 2 is ellipse, then the value range of M is?

In the plane rectangular coordinate system, if the curve represented by the equation m (x ^ 2 + y ^ 2 + 2Y + 1) = (x-2y + 3) ^ 2 is an ellipse, the value range of M (x ^ 2 + y ^ 2 + 2Y + 1) = (x-2y + 3) ^ 2 = = > m (x ^ 2 + (y + 1) ^ 2) = (x-2y + 3) ^ 2 = = > m > 0, root sign m * root sign [x ^ 2 + (y + 1) ^ 2] = (x-2y + 3) = = > root sign (M / 5) * root sign [x ^ 2 +

How to prove prime number P | (p-1)! + 1?

Wilson theorem
Let G be the primitive root of module P,
Then G ^ 1, G ^ 2,..., G ^ (p-1) are not the same with respect to module P, that is, they just form 1,2,..., P-1 with respect to module P
therefore
(p-1)!=g^1 * g^2 * ... * g^(p-1) = g^{p(p-1)/2}= {g^(p-1)}^{(p-1)/2} * g^{(p-1)/2}.
And G ^ (p-1) = 1 (mod p) Fermat small theorem
G is the primitive root, so G ^ {(p-1) ^ 2}! = 1 (mod p), the multiplication of module P is a multiplication group, x ^ 2 = 1, and X! = 1 then x = - 1
So G ^ {(p-1) ^ 2} = - 1 (mod p)
That is (p-1)! = - 1 (mod p)

The monotone decreasing interval of function f (x) = 2x2-3 | x | is______ ．

The function f (x) = 2x2-3 | x | = 2x2 − 3x (x ≥ 0) 2x2 + 3x (x < 0) is shown in the figure below. The subtraction interval of F (x) is (- ∞, - 34] and [0, 34]. So the answer is: (- ∞, - 34] and [0, 34]

If the function f (x) = LG (1-x2) is meaningful in X ∈ [0, a], find the range of the function

It is known that: (1-x2) > 0
Then - 1

Please write a program to find the sum of prime numbers, for example, f (7) = 1 + 3 + 5 + 7 + 11 + 13 + 17 = 58

There is something wrong with your question. 1 is not a prime number
Give you an idea, if you are learning C on their own operation. Copy others is meaningless
Define that the number in the array cannot be divisible by 235. (when a number read is divided by 235, if it is equal to an integer, the loop will continue, if it is not equal to an integer, it will be added to the formula.) then read the next number until the reading is finished

Let the probability density of random variable X be f (x) = 0.5cos (x / 2)
Suppose that the probability density of random variable x is f (x) = 0.5cos (x / 2), 0 ≤ x ≤ π, observe x four times independently, and use y to express the number of times that the observed value is greater than π / 3, then calculate the mathematical expectation of Y ^ 2

If x is observed once independently, the probability that the observed value is greater than π / 3 is p = ∫ (π / 3) > π) 0.5cos (x / 2) DX = 1-sin (π / 6) = 1 / 2. If x is observed four times independently, it is four independent experiments. The probability is binomial distribution B (4, K, 1 / 2). Therefore, the distribution of Y and Y ^ 2 is y 0.123 4 y ^ 20 1.49 16b (...)

Given that the quadratic function f (x) = AX2 + BX satisfies f (x-1) = f (x) + X-1, the analytic expression of F (x) is obtained

What is the greatest common factor of 10 and 18?

2

For rational numbers a and B, define the operation: a △ B = 3A + B / a-3b, calculate (- 2) △ 7 △ 6]
The question is in the second chapter of "class assignment" in the first grade of junior high school,

（—2）△[7△（—6）]
=(-2)△[7*3+7/6-3*6]
=-2△25/6
=-2*25/6+25/3-25/2
=-25/3+25/3-25/2
=12.5