On the quadratic equation of one variable It is known that a, B and C are the three sides of triangle ABC, and the univariate quadratic equation (a + b) x ^ - 2cx - (a-b) = O of X has two equal real roots. Please judge the shape of triangle ABC

On the quadratic equation of one variable It is known that a, B and C are the three sides of triangle ABC, and the univariate quadratic equation (a + b) x ^ - 2cx - (a-b) = O of X has two equal real roots. Please judge the shape of triangle ABC

The condition of having equal real roots: (2C) ^ - [- 4 (a + b) (a-b)] = 0
The solution of the equation is: C ^ + A ^ - B ^ = 0
b^=a^+c^
So it's a right triangle
B ^ = a ^ + C ^ isosceles right angle RT
What's the matter with children now? We need to ask such a simple question
1、 For the equation of X, when m = (), it is a bivariate equation
(1) (M-4) xsquare - (m-2) x + M-1 = 0
(2) (M's square-4) x's Square - (m-2) x + (m-1) = 0
The equation is a quadratic equation with one variable, and the coefficient of quadratic term is not equal to 0
(1)
m-4≠0
m≠4
When m ≠ 4, the equation is quadratic
(2)
m²-4≠0
m²≠4
M ≠ 2 and m ≠ - 2
When m ≠ 2 and m ≠ - 2, the equation is quadratic
(1) (M-4) xsquare - (m-2) x + M-1 = 0
M is not equal to 4
(2) (M's square-4) x's Square - (m-2) x + (m-1) = 0
M is not equal to plus or minus 2
1. M4 is a bivariate equation.
2. M2, m-2 is a quadratic equation with one variable. Ask: that, I don't understand. What is it?
The problem of quadratic equation with one variable
x（2x-5）=4x-10
x（2x-5）=4x-10
2x*x-5x=4x-10
2x*x-5x-4x+10=0
2x*x-9x+10=0
Split:
2 -5
X
1 -2
The original equation can be reduced to:
(2x-5)(x-2)=0
Then, 2x-5 = 0 or X-2 = 0
The solution is x = 5 / 2 or 2
Solving practical problems with equations
It takes 3 hours for Party A to do a job alone, and 4 hours for Party B to do it alone. After half an hour of cooperation between Party A and Party B, the rest of the work will be completed by Party B alone. How many hours will it take?
It will take x hours to set up
（1/3+1/4）×0.5+1/4x=1
7/24+1/4x=1
1/4x=17/24
x=17/6
A: it will take 17 / 6 hours to complete
It will take x hours to set up
（1/3+1/4）×0.5+1/4x=1
7/24+1/4x=1
1/4x=17/24
x=17/6
A: it will take 17 / 6 hours to complete
It will take x hours to complete the design.
1/4x=1-（1/3+1/4）×1/2
1/4x=17/24
x=17/6
Let X be r, let a = 2x square + 1, B = 3x-4, then the size relation of a and B
Let X be r, let a = 2x square + 1, B = 3x-4, then the size relation of a and B
A = 2x square + 1, B = 3x-4
A-B = 2x square + 1 - (3x-4)
=2X + 1-3x + 4
=2x-3x + 5
=2 (x-3 / 4) + 31 / 8 > 0
therefore
A>B
It is divided into three parts: greater than 0, less than 0, and equal to 0
Brother! When x equals one! You're in the first place! Why don't you just come out? Don't ask such a simple question in the future!
The time of use price of Wuhu power supply company can be divided into two periods: the average period is 8:00-22:00, 14 hours, and the valley period is 22:00-8:00 the next day, 10 hours. The average electricity price rises by 0.03 yuan per kilowatt hour on the basis of the original sales price, and the valley electricity price falls by 0.25 yuan per kilowatt hour on the basis of the original sales price The electricity price for each section is 60 kwh, and 42.73 yuan is paid according to the time of use electricity price. (1) how many yuan are the average section and valley section electricity prices paid by Xiao Ming in that month? (2) If the time of use price is not used for settlement, how much more will Xiaoming pay in May?
(1) Suppose the original sales price is x yuan per kilowatt hour, according to the meaning of the question: 40 × (x + 0.03) + 60 × (x-0.25) = 42.73, the solution is: x = 0.5653 〉 when x = 0.5653, x + 0.03 = 0.5953; x-0.25 = 0.3153 Mingjia will pay 13.8 yuan more in May
Calculation [(3x / (X-2)) - (x / (x + 2))] · ((X & # 178; - 4) / x)
The original formula = [3x / (X-2) - X / (x + 2)] · ((X-2) (x + 2) / x)
=3(x+2)-(x-2)
=2x+8
2X^5-8X^4-8X^3-32X^2
Let's divide the denominator in brackets first...
The original formula = [3x (x + 2) - x (X-2)] / (X & # 178; - 4) · [(X & # 178; - 4) / x]
=(2X²+8X)/X
=2X+8
Solving practical problems with the first equation of junior high school
When a person goes out at six o'clock in the evening, the angle between the hour hand and the minute hand is 55 degrees. When he comes home, he finds that it is not 7 o'clock, and the angle between the hour hand and the minute hand is still 55 degrees
When the hour hand speed is 360 / 12 * 60 = 0.5 ° per minute and the minute hand speed is 360 / 60 = 6 ° at 6 o'clock, the hour hand is 180 ° ahead of the minute hand. Set the angle between the hour hand and the minute hand to be 55 ° after X minutes, then 180-55 = (6-0.5) * x solves x = 250 / 11, which is the departure time. Similarly, set the return time to be y, then 180 + 55 =
Using factorization method to solve the equation: 3x (x-1) = 2-2x
3x (x-1) + 2 (x-1) = 0, (x-1) (3x + 2) = 0, X-1 = 0 or 3x + 2 = 0, so X1 = 1, X2 = - 23
A and B run on the same circular track. A runs a circle in 40 seconds, B runs a circle in 24 seconds
(1) How long does it take for each encounter?
(2) Start at the same place, run in the same direction, and meet again after a few seconds?
The idea of engineering problems is applied to encounter and pursuit problems
（1）1/(1/40+1/24)
Two people walk a whole journey together. Divide the total distance by speed and speed
(2)1/(1/24-1/40)
When we meet again, B runs one more lap than a, and the distance difference is divided by the speed difference
How many meters in a circle? Question: the question does not say... It is too simple..