Several factorizations (square difference formula) 1) X square y square Z square 2) 9 / 4m square - 0101n square 3) 16 (a-b) square - 9 (a + b) square 4) 25p square - 49q square 5) 4A square - (B + C) square

Several factorizations (square difference formula) 1) X square y square Z square 2) 9 / 4m square - 0101n square 3) 16 (a-b) square - 9 (a + b) square 4) 25p square - 49q square 5) 4A square - (B + C) square

At the same time, we can't understand 3. = [4 (a-b) [[4 (a-b)] [(4 (a-b); - [3 (a + b) [[3 (a + b)] [[3 (a + b)] [(3 (a-b)] [(178); [3 (a-b); = [4 (a-b) = [4 (a-b) + (3 (a-b) + 3 (a + b) [(XY + Z) (XY + Z) (xy-z) (xy-z) (xy-z) (xy-z) (xy-z) (xy-z) (xy-z) 2) 2.we can not understand 3. = [4 (4 (a-b) [[4 (a-b) (4 (a-b) [(4 (a-b) [(4 (4 (a-b) [(4 (a-b) [[4 (a-b) [(4 (a-b) [(4 (a-b) [(4 178; = [(2a + (B + C)] [(2A - (...)
1. Primitive = (XY + Z) (xy-z)
2. The original formula = (2m / 3 + n) (2m-n) What is 0101 after this question?
3. The original formula = [4 (a-b) + 3 (a + b)] [4 (a-b) - 3 (a + b)] = (7a-b) (a-7b)
4. The original formula = (5p + 7q) (5p-7q)
5. Original formula = (2a + B + C) (2a-b-c)
Compare the sizes of 3x ^ 2 and 2x-1
Title, such as
It's better to use the comparative method
Let f (x) = 3x ^ 2 - (2x-1);
Then f (x) = (- 3x + 1) * (x + 1)
It can be concluded that: 1. When x = 1 / 3 and - 1, they are equal;
2. When - 1
How can matlab solve this equation?
v=35.01;T=973;p=0.21;
K1=6.528*10^-3*exp(-149000/(8.314*T));K2=5*10^-3*exp(-150000/(8.314*T));
K3=10^-3*exp(-210000/(8.314*T));K4=3.24*10^-8*exp(-1371.3/T);
a=K1*p^0.5;b=K2*p^0.5;c=K3^2*p^1.5;d=K4*p^0.5;
X = solve ('2 / V * x / (x ^ 2 + a) + 0.8 / V * x / (x ^ 2 + b) + 3 * x ^ 5 * (sqrt (1 + 1.2 * C / (x ^ 6 * V)) - 1) / C + 6 / V * x / (x ^ 2 + D) = 1 ','x'). How to solve this equation and how to assign values to a, B and C
I tried to draw a picture of the function as if it had no solution
f=@(x)2/v*x/(x^2+a)+0.8/v*x/(x^2+b)+3*x^5*(sqrt(1+1.2*c/(x^6*v))-1)/c+6/v*x/(x^2+d)-1
fplot(f,[-100,100])
Mathematical problems: square difference formula & complete square formula
1. Change (x + 2y-3) (x-2y-3) to________ It can be calculated by square difference formula
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
(x+2y-3)(x-2y-3)=[(x-3)+2y]*[(x-3)-2y]
(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x^2-y^2)^2-(x^2-y^2)(x^2+y^2)
=(x^4-2x^2 *y^2+y^4)-(x^4-y^4)
=-2x^2*y^2+2y^4
1. Changing (x + 2y-3) (x-2y-3) to [(x-3) + 2Y] [(x-3) - 2Y] can be calculated by square difference formula
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x-y)(x+y)[(x+y)(x-y)-(x²+y²﹚]
=-2Y & # 178; (x + y) (X-Y) 1. [x + (2y-3)] [x - (2Y + 3)... Expansion
1. Changing (x + 2y-3) (x-2y-3) to [(x-3) + 2Y] [(x-3) - 2Y] can be calculated by square difference formula
2.(x+y)²(x-y)²-(x-y)(x+y）(x²+y²)
=(x-y)(x+y)[(x+y)(x-y)-(x²+y²﹚]
=-2Y & # 178; (x + y) (X-Y) ask: 1. [x + (2y-3)] [x - (2Y + 3)] OK
2-3x = 1 / 2 (1 / 4-2x) find x
X equals 15 / 16
What is the solution and root formula of quadratic equation with one variable in junior high school?
Generally speaking, the solutions of quadratic equation of one variable are: (Note: the following ^ means square.)
1、 For example: x ^ 2-4 = 0
x^2=4
X = ± 2 (because x is the square root of 4)
∴x1=2,x2=-2
2、 For example: x ^ 2-4x + 3 = 0
x^2-4x=-3
Formula, get (with the square of half of the first term coefficient)
X ^ 2-2 * 2 * x + 2 ^ 2 = - 3 + 2 ^ 2
(X-2) ^ 2 = 1
x-2=±1
x=±1+2
∴x1=1,x2=3
3、 Formula method (the formula of formula method is derived from formula method)
-B ± ∫ B ^ 2-4ac (- B addition and subtraction followed by B ^ 2-4ac under the root)
The formula is: x = - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
2A
(b ^ 2-4ac) under the - B ± root sign of 2A
First of all, we should make clear what is a, B and C
In fact, they are the most standard form of binary linear equation: ax ^ 2 + BX + C = 0
Δ = B 2-4ac is called the discriminant of the root of the equation
When b2-4ac > 0, the equation has two unequal real roots;
When b2-4ac = the equation has two equal real roots;
When b2-4ac
What is the square difference formula in mathematics? There is also the complete square formula
(a+b)(a-b)=a^2-b^2
(a±b)²=a²±2ab+b²
Given X & # 178; - 2x = 1, find the value of (x-1) (3x + 1) - (x + 1) &# 178
x²－2x＝1
x²-2x-1=0
﹙x－1﹚﹙3x＋1﹚－﹙x＋1﹚²
=3x²-2x-1-x²-2x-1
=2x²-4x-2
=2（x²-2x-1）
=0
Who can help me to solve the problem of the root formula of quadratic equation of one variable
Note: don't make it too difficult
More than a few, as long as the solution of quadratic equation, do not fill in the blanks, choice and application problems
Help me with the problem. I want to do it
More points, root formula, the more the better
Test questions of quadratic equation of one variable
The full score of this paper is 100, and the examination time is 100 minutes
1、 Fill in questions: (2 '× 11 = 22')
1. The root of equation x2 = is
2. The general form of equation (x + 1) 2-2 (x-1) 2 = 6x-5 is
3. On the univariate quadratic equation x 2 + m x + 3 = 0 of X, if one root is 1, then the value of M is
4. It is known that the quadratic trinomial x2 + 2mx + 4-m2 is a complete square, then M =
5. Given + (B-1) 2 = 0, when k is, the equation kx2 + ax + B = 0 has two unequal real roots
6. If the equation mx2-2x + 1 = 0 of X has only one real root, then M =
7. Please write one root as 1 and the other root satisfies - 1
Formula:
aX^2+bX+c=0
(-b+sqr(b^2-4ac))/2a
(-b-sqr(b^2-4ac))/2a
The relationship between the root and coefficient of quadratic equation with one variable
1、 Fill in the blanks
Then the two equations of α and β are 1=__________ ，αβ=__________ ， __________ ， __________。
2. If 3 is one root of the equation, then the other root is__________ ，a=__________。
3. If the two equations are - 3 and 4, then AB =.
4. The quadratic equation with sum as root is__ ... unfold
The relationship between the root and coefficient of quadratic equation with one variable
1、 Fill in the blanks
1. If α and β are two parts of the equation, then α + β=__________ ，αβ=__________ ， __________ ， __________。
If the other root is 2__________ ，a=__________。
3. If the two equations are - 3 and 4, then AB =.
4. The quadratic equation of one variable with the root of sum is.
5. If the length and width of the rectangle are two of the equations, then the perimeter of the rectangle is__________ , with an area of.
6. If the reciprocal sum of the roots of the equation is 7, then M = uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu.
2、 Multiple choice questions
1. The equation satisfying the sum of two real roots is 4.
（A） （B）
（C） （D）
2. If k > 1, then the case of the root of the equation about X is ().
(A) There is a positive root and a negative root (b) has two positive roots
(C) There are two negative roots (d) and no real roots
3. Given that the sum of two numbers is - 6 and the product of two numbers is 2, then the two numbers are ().
（A） ， （B） ，
（C） ， （D） ，
4. If the absolute value of the difference between the two equations is 8, then the value of P is ().
（A）2 （B）-2
（C）±2 （D）
3、 Answer questions
1. Two real roots of the equation are known, and the value of K is obtained.
2. Solve the equation and find a new quadratic equation of one variable so that its two parts are the square of the two parts of the equation.
3. If the two real roots of the equation about X are less than 1, find the value range of M.
4. What is the value of M
(1) The two are reciprocal to each other;
(2) It has two positive roots;
(3) There is a positive root and a negative root.
Reference answer
1
1．1， ，2，-2
2．-2，-1
3．-48
4．
5．6，
6．
2
1．B
2．B
3．D
4．C
3
1．1
2．
3．
4．（1）m=-1
（2）-1≤m＜0
(3) M ＞ 0
Factorization (X & # 178; + 4) &# 178; - 16x & # 178;
(x²+4）²-16x²
=(x²+4）²-(4x)²
=(x²+4+4x)(x²+4-4x)
=(x+2)²(x-2)²
(x²+4)²-16x²
= (x²+4x+4) (x²-4x+4)
= (x+2)² (x-2) ²
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