It is known that the equation (m ^ 2-4m + 5) x ^ 2 + (2m + 1) X-1 = 0 about X. proof: no matter what the value of M is, the equation is a univariate quadratic equation about X 2. No matter what the value of M is, the equation always has two unequal real roots

It is known that the equation (m ^ 2-4m + 5) x ^ 2 + (2m + 1) X-1 = 0 about X. proof: no matter what the value of M is, the equation is a univariate quadratic equation about X 2. No matter what the value of M is, the equation always has two unequal real roots

one
The quadratic coefficient is m ^ 2-4m + 5 = m ^ 2-4m + 4 + 1 = (m-2) & sup2; + 1
Therefore, the coefficient of quadratic term is not 0, that is, no matter what the value of M is, the equation is a quadratic equation of one variable about X
two
（M^2-4M+5)X^2+(2M+1)X-1=0.
△=(2M+1)²+4（M^2-4M+5）
=4M²+4M+1+4M^2-16M+20
=8M^2-12M+21
Let w = 8m ^ 2-12m + 21
Then △ '= (- 12) & sup2; - 32 * 21 = - 528
So w is always greater than 0, because the quadratic coefficient is greater than 0 and the discriminant is less than 0
So the above △ = 8m ^ 2-12m + 21 is always greater than 0
So no matter what the value of M is, the equation always has two unequal real roots

It is known that the equation (m-2) x2 + 4x + m2-4m = 0 has a root of 1

x=1
Then m-2 + 4 + M & # 178; - 4m = 0
m²-3m+2=0
(m-1)(m-2)=0
For quadratic equation of one variable, then x & # 178; coefficient m-2 ≠ 0
So M-1 = 0
m=1

There are 5400 tons of coal in a pile. Two fifths of the coal is used in the first month and four ninths in the second month. How many tons are left?
Using fractional mixed operations and solving equations, there must be both

1) 5400 * (1-2 / 5-4 / 9) = 840 tons
2) We have X tons left
x/5400=(1-2/5-4/9)
X = 840 tons

The problem of mean value inequality in senior one
Given x ^ 2 + y ^ 2 = 1, find the value range of 2x + y

x=sina
y=cosa
2x+y=2sina+cosa
=Root 5sin (a + b)
Value range - root 5

After 10 hours of meeting, it is known that the bus is 20% faster than the truck. What is the speed of the train

Speed and 1100 △ 10 = 110 km
The speed of freight car is 110 (1 + 20% + 1) = 50 km

1. On 56x & # 178; + ax-a & # 178; < 0
2.2x-5!x+1!＜2

The first question is written in the form of a cross
7 a
8 -a
So the original inequality is (7x + a) (8x-a)

The speed of a train is 80% of that of a passenger car. A freight car and a passenger car run from each other. After five o'clock, the two cars meet. The distance ratio of the freight car and the passenger car is (): ()

Distance ratio 80%: 1 = 4:5
If you don't understand this question, you can ask,

If a (- 7,0), B (7,0) and C (2, - 12) are known, if C is the focus of the ellipse,
And passing through two points a and B, the track of the other focus D of the ellipse is (please give the steps)

The square of the distance between AC is 225, and the square of the distance between BC is 169
Let the coordinates of point d be (x, y)
[x-(-7)]*[x-(-7)]+(y-0)*(y-0)+225=(x-7)*(x-7)+(y-0)*(y-0)+169
Because CD is the two focal points of the ellipse, and the sum of the distances between any point on the ellipse and the two focal points of the ellipse is certain, there is: AC + ad = BC + BD

The two baskets of apples weigh 195kg in total. If 3 / 7 of them are taken out of basket a and 75 kg are taken out of basket B, then the two baskets are the same weight. How many kg is basket a,
How many kilos,

Let a be x and B be y
have to
X+Y=195
4/7X=Y-75
X=76
Y=119

What's the date of 40 days from today?
Today is August 16. What's the date in 40 days?

40 days after September 25, 2011 and August 16, 2011