No matter what the value of M is, does the equation 2 times the square of X - (4m-1) the square of x-m-m-m = 0 have two unequal real roots? Why? Let (x + m) be the square of (x + m) + n Square of x-2x-3 = (x -) square + () Square of X + PX + q = (x +) square + () Solve the following equation The square of (4x-1) - 10 (4x-1) - 24 = 0 The square of (3x-2) = 9x Solve the equation and judge the root of the following equation: 2 times the square of X - 5x + 1 = 0 5x（5x-2）=-1 Square of (x-4) + 2 (x + 1) = 0 Square of X + square of 2x-m = 0 (M is a known number) The length of a rectangular open space is 24 meters and the width is 12 meters. Now we need to draw a small rectangular area in the center of it to plant flowers, and plant grass around the rest. If the width of the four sides is the same, the area of the small rectangle is 5 / 9 of that of the original rectangle, How many meters are the length and width of the small rectangle? Square of (x-a) = 4 (square of x-a) (a is a known number) It's a process!!! Process process!!! Do all the questions!!! Urgent demand!!!

No matter what the value of M is, does the equation 2 times the square of X - (4m-1) the square of x-m-m-m = 0 have two unequal real roots? Why? Let (x + m) be the square of (x + m) + n Square of x-2x-3 = (x -) square + () Square of X + PX + q = (x +) square + () Solve the following equation The square of (4x-1) - 10 (4x-1) - 24 = 0 The square of (3x-2) = 9x Solve the equation and judge the root of the following equation: 2 times the square of X - 5x + 1 = 0 5x（5x-2）=-1 Square of (x-4) + 2 (x + 1) = 0 Square of X + square of 2x-m = 0 (M is a known number) The length of a rectangular open space is 24 meters and the width is 12 meters. Now we need to draw a small rectangular area in the center of it to plant flowers, and plant grass around the rest. If the width of the four sides is the same, the area of the small rectangle is 5 / 9 of that of the original rectangle, How many meters are the length and width of the small rectangle? Square of (x-a) = 4 (square of x-a) (a is a known number) It's a process!!! Process process!!! Do all the questions!!! Urgent demand!!!

1. No matter what the value of M is, does the equation 2 times the square of X - (4m-1) the square of x-m-m = 0 have two unequal real roots? Why?
Consider the equation multiplied by the square of X - (4m-1) the square of x-m-m-m = 0, the discriminant = (4m-1) ^ 2 + 4m = 16m ^ 2-4m + 1 = (4m-1 / 2) ^ 2 + 3 / 4 > 0, so no matter what the value of M is, the square of X - (4m-1) the square of x-m-m-m-m-m = 0. There are always two unequal real roots
2. Make the following formula square of (x + m) + N:
The square of x-2x-3 = (x-1) + (4)
Square of X + PX + q = (square of X + 2 / P) + (square of q-4 / P)
3. Solve the following equation
(1) The square of (4x-1) - 10 (4x-1) - 24 = 0
(2) The square of (3x-2) = 9x
(1) Let 4x-1 = a
Then the square of a-10a-24 = 0
The square of a - 10A + 25-49 = 0
Square of (a-5) = 49 [Formula]
A-5 = plus or minus 7
a1=12 a2=-2
(2) The square of 9x - 12x + 4 = 9x
The square of 9x - 21x + 4 = 0
Using the root formula, we get X1 = 6 (7 + root 33), X2 = 6 (7-root 33)
4. Solve the equation and judge the following equation roots:
2 times the square of X - 5x + 1 = 0 [the square of discriminant = (- 5) - 4 * 2 * 1 = 17 is greater than 0, so there are two unequal real roots]
5x (5x-2) = - 1 [reduced to 25X square - 10x + 1 = 0, discriminant = (- 10) square - 4 * 25 * 1 = 0, so there are two equal real roots]
The square of (x-4) + 2 (x + 1) = 0 [reduced to the square of X - 6x + 18 = 0, the square of discriminant = (- 6) - 4 * 1 * 18 = - 36 is less than 0, so there is no real root]
Square of X + square of 2x-m = 0 (M is a known number)
[discriminant = the square of 2 + the square of 4 * m = the square of 4 + 4 * m, because the square of M is greater than 0, so the discriminant is greater than 0, so there are two unequal real roots]
5. The length of a rectangular open space is 24 meters and the width is 12 meters. Now we need to draw a small rectangular area in its center to plant flowers, and plant grass around the rest. If the width of the four sides is the same, and the area of the small rectangle is 5 / 9 of that of the original rectangle, how many meters are the length and width of the small rectangle?
The area of small rectangle is 5 / 9 of that of large rectangle, so the area of small rectangle is s = 24 * 12 * 5 / 9 = 160
The area of large rectangle is 24 * 12 = 288
Then the area of the four sides is 288-160 = 128
The width of grassland is x, with X * x * 4 + (24-2x) * x * 2 + (12-2x) * x * 2 = 128
The push out width is x = 2
Then the length of the small rectangle is a = 24-2x = 20 (m); the width is b = 12-2x = 8 (m);
6. (x-a) square = 4 (x-a-a) (a is known)
(x-a)(x-a)=4(x+a)(x-a)
When x-a = 0, i.e. x = a, the equation has a solution x = a
When x-a is not equal to 0, that is, X is not equal to a, the equation is changed to:
x-a=4x+4a
-3x=5a
X = - 5 / 3
[this question needs to be discussed by category]