Middle School Math Problems 1 Yuan 2 Equations

I know: because p 2-p+>=0 is true. (as can be seen from p 2-p + > = 0).

So collated as p 2+q>=p+; That is, the two sides of the equation + q are moved again.

It is easy to get from the initial conditions: p 2 + q < 0; (the judgment condition of the root) can be pushed out p+<0; [Because the two numbers (p 2 + q) (p + medium, the big one (p 2 + q) is smaller than 0, and the small one (p + is definitely smaller than 0.) 】

Proven. (Actually, I came to the conclusion based on the above reverse reasoning, you can give it a try).

Junior high school and I won't drop.

I mean, it shouldn't be that hard.

The problem is not less conditional: the solution of the equation is less than -1 2

Because p 2-p+>=0 is true. (as can be seen from p 2-p + > = 0) so it is arranged as p 2 + q > = p +; That is, the two sides of the equation + q are moved again.

It is easy to get from the initial conditions: p 2 + q < 0; (the judgment condition of the root) can be pushed out p+<0; [Because the two numbers (p 2 + q) (p + medium, the big one (p 2 + q) is smaller than 0, and the small one (p + is definitely smaller than 0.) Proven.

The previous equation is added to give the vertical trace 3(a1+a2)+4(b1+b2)=c1+c2

Second, the sum of the cheating equation gives 3(a1+a2)x+4(b1+b2)y=5(c1+c1).

C1+C2 in the second secant of the first middle fiber family, the coefficients are the same as x=5 and y=10

Solution: (m-1)x-square+2mx+(m+3)=0 (m is not equal to 1).

Known: x + xy + y = 14, y + xy + x = 28, find the value of x+y.

When k is an integer, the two roots of the unary quadratic equation kx -(2k+3)x+6=0 are integers.

You've figured out all the cases of ax +bx+c=0, and you're pretty much at this stage.

I'm a teacher. Topics and the like can be made up and then sought.

According to the problem: 1 a+1 b-1 (a-b)=0 solution: (a+b) (ab)=1 (a-b).

a+b)(a-b)=ab

a²-b²＝ab

i.e.: a -ab-b = 0

Divide both sides by b to get:

a/b)²-a/b)-1=0

Let a b=x, and the original formula is: x -x-1=0

Solution: x=(1 5) 2

i.e.: a b = (1 5) 2

However, since a and b are both negative, a b > 0

a/b=(1+√5)/2

Finding the Root Formula According to a Quadratic Equation!

In equation: a -ab-b 0.

1) Treat a as an unknown x and b as a known number, and the equation can become:

x²-bx-b²=0

x=(1±√5)b/2

2) Treat b as an unknown number x and a as a known number, and the equation can become:

a²-ax-x²=0

i.e.: x -ax-a = 0

x=(1±√5)a/2

a -ab-b =0 = b +ab-a =0 with a as a known number, then b=(-a+ or - under the root sign (a +4a)) 2 puts a is it.

Can you understand this? It's clearer to write on paper with a pen.

He regarded the equation a -ab-b =0 as a quadratic equation about b, and then used the root finding formula to solve that the two roots of b are (-1 5) 2*a, because a < 0, b should also be less than 0, so b = (-1 + 5) 2*a

a2-ab-b2=0, after this step.

Since b is not 0, both sides of the equation are divided by b2 at the same time, and then a b is treated as a whole.

It is better to let a b=x, then the original formula becomes x 2-x-1=0, which is a one-dimensional quadratic equation, which you can solve. The value of x is what you want.

Note: After the solution, x has two values, and it is known from the problem that a and b are both negative numbers, so x > 0, that is, a b>0

Think of b as an unknown, which is equivalent to x; If you take a as a known number, you can get the above result!

There is an easier way to solve the problem:

1.After the original formula of the question is scored, the score (a -ab-b) = 0;

2.Because the fraction is not equal to 0, we get a -ab-b = 0;

3.Divide the whole equation by a, and then solve a b as an unknown, and you get! If we know that a and b are both negative real numbers, we get b = -1 + change sign 5 when we remove the negative value and get the b= -1 + change sign 5

He treats a as a constant and b as an unknown, and solves a quadratic equation.

It can also be solved as follows: let a b = k get a = bk and substitute a -ab-b = 0 to get (k -k-1) b = 0

Because b is the denominator and cannot be 0, therefore: k -k-1 = 0 is solved to get k = -(1 + 5) 2 or k = (-1 + 5) 2 Because a and b are both negative real numbers, k > 0, so k = (-1 + 5) 2k is a part of b

a²-ab-b²=0

That's what I wanted.

b -ab+a =0 takes a as a known number and b as an unknown number to solve a quadratic equation.

Discriminant = (-a) 2-4*(-1)*a = 5a submergetic root formula.

1.The equation should be: (a-21)(350-10a)=400 solution: a=25 or 31

a<21*(1+20%)

So a <

So a=25

Therefore, the number of items that need to be sold is (350-10a) = 350-10 * 25 = 100 (pieces).

The selling price of each item = a = 25 (yuan).

A: The number of items to be sold is 100 pieces, and the price of each item should be 25 yuan.

1.Sell 100 items, and sell 25 yuan for nothing.

2.The ticket price should be set at 40 yuan.

3.At 70 yuan**, 600 pieces of clothing are imported every day.

If the worker making part A is x and the worker is y, then the person making part C is (86 x y).

A total of 5x parts were made; A total of 4y pieces of B parts were made. A total of 3 (86 x y) parts were made.

5x/3＝4y/2＝3（86－x－y）

Solution x 36, y 30

Answer: There are 36 workers to make parts A, 30 workers to make parts B, and 20 workers to make parts C, so that the three parts made are just matched.

Set up a person x, a person y, and a person c (86-x-y).

5x/3=4y/2=3（86-x-y）

Solution x 36, y 30

So 36 workers are used to make parts A, 30 workers are workers for parts B, and 20 workers are used for parts C.

3:2:1 6 set.

See the 60:6 relationship 86 12 = 7....2

21 28 35 2 Cooking rice left.

A total of 5x parts were made; A total of 4y pieces of B parts were made. A total of 3 (86 x y) parts were made.

5x/3＝4y/2＝3（86－x－y）

Solution x 36, y 30

Answer: There are 36 workers to make parts A, 30 workers to make parts B, and 20 workers to make parts C, so that the three parts can be matched exactly.