Headache help me The parabola y = ax ^ 2 + HX + C intersects with the negative half axis of X axis. The positive half axis intersects with A.B The positive half axis of y-axis intersects with C and ob = 2oC = 2oa 1. Find the value of the algebraic expression ABC 2. If the line Y-X + B passes through point C For all real numbers, the value of the algebraic formula ax ^ 2 + BX + C is not greater than 9 / 16 HELP I have already Give it to whoever leaves a message arbitrarily..

1. First of all, it's easy to think of △ amn ∽ ABC
∷
Let the height of Mn in △ amn be H
The equation is as follows
x:10=h:5
h=x/2
Then area = x × H = (x ^ 2) / 4
∷
Or in a simple way
"Area ratio equals the square of similarity ratio"
x^2:10^2=s：25
We can also get s = (x ^ 2) / 4
2. Are there any missing letters in the title?
Fold along M
There is something wrong with this sentence
How to fold along the point?
If it's Mn
Y=s=(x^2)/4
Because A2 is in mnbc
So Mn should be above the median line of △ ABC (including the median line)
That's x0
That is 0

We know the equation about X. the square of x minus 2 times K-3 times x plus the square of K
If the two roots of the equation x minus 2 times the bracket K-3, x plus the square of K minus 4K minus 1 = 0 are taken as the abscissa, and the point of the ordinate is just on the pattern where the inverse scale function y is equal to m / x, the minimum value of M satisfying the condition can be obtained

x^2-2(k-3)x+k^2-4k-1=0
Two X + y = 2 (K-3)
xy=k^2-4k-1
M=xy=(x+y+2)^2/4-5
X + y + 2 = 2 times radical (XY + 5) > = 2 + 2 times radical (XY)
xy

The system of equations x + y = 1, x + K square multiplied by y = K. there is a unique solution, find the value of K

The equation has a unique solution, so the equation YK ^ 2 - K + x = 0 is a complete square
So, 2 √ (XY) = 1
XY=1/4.
X+Y=1
By solving the above equations: x = 1 / 2, y = 1 / 2, and substituting into k equation: x = 1 / 2, y = 1 / 2
√（1/2）K-√（1/2）=0
K=1

(x square - (K + 3) times x + k-1 = 0 to find the root of the equation

△=[-(k+3)]²-4(k-1)
=k²+6k+9-4k+4
=k²+2k+1+12
=(k+1)²+12>0
So the equation has two unequal real roots

① How many different solutions are there for 5x + 10Y = 40? 2 write out a group of integer solutions, a group of negative integer solutions and a group of positive integer solutions for the quadratic equation 4x-3y = 15
③ Find the nonnegative solution of the binary linear equation 2x + 3Y = 20, and transform the following equation into y (1) x = 2 / 3 × Y-1 (2) 3 / x-4 / y = 5 with the formula of X

① 5x + 10Y = 40, there are (innumerable) different solutions
② Write a group of integers x = 6, y = 3 of quadratic equation 4x-3y = 15
A group of negative integer solutions x = - 3 y = - 9
A group of positive integer solutions x = 6, y = 3
③ Finding the nonnegative solution of the quadratic equation 2x + 3Y = 20
x = 1 y = 6
x=7 y=2
(1) X = 3 / 2 × Y-1
x+1 = 3y/2
3y = 2x+2
y = (2x+2)/3
(2) 3 x-4 y = 5
4x- 3y = 60
3y = 4x-60
y = (4x-60)/3
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For the quadratic equation 4x + 5Y = 98,4x + 2 = 5Y, find x =, y = 2x + 5Y = 98,4x + 2 = 5Y, find x =, y = "

4X + 5Y = 98 when x = 12
4x+4x+2=98 4x+5y=98
8x+2=98 4×12+5y=98
8x=96 48+5y=98
x=12 5y=50
y=10
A: x = 12, y = 10

The following equation of degree 1 with 2 variables 4x-y = 9,3x + 5Y = 24 is solved by substitution method

Y = 4x-9
Substituting the two formulas, we get 3x + 5 (4x-9) = 24
23x=69
x=3
y=4x-9=3

When a and B solve the binary linear equation () x + 5Y = 13 (1), 4x + () y = - 2 (2), a misread the coefficient of X in equation (1),
When a and B solve the binary linear equation () x + 5Y = 13 ① 4x + () y = - 2 ②, a misinterprets the coefficient of X in equation ①, and gets x = 107 / 47, y = 58 / 47; B misinterprets the coefficient of Y in equation ②, and gets x = 81 / 76, y = 17 / 19. If both of them are correct in calculation, please write down this equation and find out the solution of this equation. After thinking for a long time, the more calculation, the more suspense. Tonight's homework will be handed in tomorrow,

Let the coefficients of X and y be a and B respectively. Since a and B have not read the wrong equations 1 and 2 respectively, they have 4 * 107 / 47 + b * 58 / 47 = - 2 and a * 81 / 76 + 5 * 17 / 19 = 13, and the solutions are b = - 9 and a = 2 respectively. So the equations are 2x + 5Y = 13, ① 4x-9y = - 2, ②.. the solutions are x = 107 / 38 and y = 28 / 19

How to solve the quadratic equation of two variables

2x+5y=17①
4x-3y=4②
The result of 2 (1) - 2 is: 13y = 30
y=30/13
Substituting y = 30 / 13 into 2, we get 4x-3x30 / 13 = 4
x=1+45/26=71/26

1. When what is the value of integer k, is the solution of equation 2kx-4 = (K + 2) x a positive integer?
2. Given that the equation a (2x-1) = 3x-2 about X has no solution, find the value of a?
3. Solve the equation: "2x-1" = 4 - "1-2x" (") is the absolute value)

1、
2kx-4=（k+2）x
2kx-4=kx+2x
kx-2x=4
x(k-2)=4
x=4/(k-2)
If x is a positive integer, we can see that K can take 3,4,6
2、
a(2x-1)=3x-2
2ax-a-3x+2=0
(2a-3)x -a+2=0
If the equation has no solution, it needs to satisfy the following conditions
The coefficient of the first term is 0, and the constant term is not 0
2a-3=0 -a+2≠0
The solution is a = 3 / 2
3、
When x > 1 / 2, it is reduced to
2x-1=4-[-(1-2x)]
2x-1=4-(-1+2x)
2x-1=5-2x
4x=6
x=3/2
When x is less than 1 / 2, it is reduced to
-(2x-1)=4-(1-2x)
-2x+1=3+2x
-4x=2
x=-1/2