On the equation kx2 + (K + 2) x + 4 / k = 0 of X, there are two unequal real number roots. Is there a real number k, so that the two real number roots of the equation are opposite numbers? If there is If it exists, find the value of K; if not, explain the reason

On the equation kx2 + (K + 2) x + 4 / k = 0 of X, there are two unequal real number roots. Is there a real number k, so that the two real number roots of the equation are opposite numbers? If there is If it exists, find the value of K; if not, explain the reason

Two numbers are opposite to each other
The sum of the two is equal to 0
That is - (K + 2) / k = 0
k=-2
When k = - 2, the original equation can be reduced to
-2x²-2=0
x²+1=0
unsolvable
There is no corresponding K value, so that the two numbers are opposite to each other

It is known that the equation kx05 + (2k-1) x + k = 0 about X has two unequal real roots. (1) find the value range of K; (2) whether there is a real number K,
Make the two real roots of the equation opposite to each other? If it exists, find the value of K; if it does not exist, explain the reason

It is known that the equation KX & # 178; + (2k-1) x + k = 0 about X has two unequal real roots. (1) find the value range of K; (2) whether there is a real number k, so that the two real roots of the equation are opposite to each other? If there is, find the value of K; if not, explain the reason
1、△=(2k-1)²-4k²>=0
-4k+1>=0
k=0

In the first PE test, 37.5% of the class got excellent results. In the second test, 9 students got excellent results. At this time, the excellent rate reached 60%, and several students were excellent

There are X students in the class
37.5%x+9=60%x
x=40 60%x=24
Now 24 people are excellent

x2+x+1/x2+1/x-4=(1/x+x+_ )(1/x+x-_ ）Factorization, thank you

Let the two blanks filled in be: A, B, then x2 + X + 1 / x2 + 1 / x-4 = (1 / x + X + a) (1 / x + X-B) = 1 / x2 + 1 + A / x + 1 + x2 + ax-b / x-bx-ab = x2 + (a-b) x + 1 / x2 + 2-aba-b = 1, 2-AB = - 4a-b = 1, ab = 6A = 1 + B 2 + B-6 = 0, B1 = - 3, B2 = 2, A1 = - 2, A2 = 3, a = - 2, B = - 3 or a = 3, B = 2

The school organized the seventh grade students to participate in the activities. The original plan was to rent 42 passenger cars, 16 of which were full. As 126 students rode bicycles, the school changed the car rental plan
(1) (2) if the speed of the bicycle is 10 km / h, and the bus runs at 40 km / h one hour after departure, the result is that all the students arrive at the designated place at the same time, how long does the bus run? (equation only)

1.
Set X vehicles to be rented
42x+126=42×16
two
The bus has been running for y hours
10(y+1)=40y

If - 2x + 14 of (4x-3) (2x-6) = a of 4x-3 + B of 2-6x, find the constants A and B
It's 2-6x

The right general denominator is
a（2-6x）+b（4x-3）=2a-6ax+4bx-3b=（4b-6a）x+（2a-3b）=-2x+14
So {4b-6a = - 2 (1)
2a-3b=14 （2）
(1) + (2) * 3
-5b=40
b=-8
Substituting (1) into the solution, a = - 5

The sum of number a, B and C is 830. Number a is 20 less than number B, and number C is 10 more than number B

(830 + 20-10) △ 3, = 840 △ 3, = 280; answer: B number is 280

Equation 1-X-1 / 2 = 2x + 1 / 3 to get the denominator? Equation x / 2-1 = x / 5 to get the denominator?
Solve the equation x-2-18x / 3 = x / 9 + 2
When what is the value of X, the value of algebraic formula 5 - (x + 2 / 3) is equal to the value of algebraic formula 7-x?
Solve the equation 2x + 1 / 3-10x + 1 / 6 = 1, remove the denominator and bracket,

1. The equation is multiplied by 6 at the same time
6-6x-3x=12x+2
2. Multiply the equation by 10 at the same time
5x-10=2x

Number a is 3 / 4 of number B, number B is 120, what's number a?
1. A piece of wire is 25 meters long. Three and one-third meters will be cut off in the first time, and the remaining four fifths will be cut off in the second time. How many meters will be cut off in the second time?
2. A cuboid box, 10 cm long, 12 and 1 / 2 cm wide, calculate the surface area and volume of the box.
3. The distance between a and B is 80 kilometers. A and B ride bicycles facing each other. A travels 7.4-1 kilometers per hour, B travels 8.8-1 kilometers per hour. How many meters is the distance between a and B in five hours?
Especially good, add 50 points directly)

Let a be x, B be y, then x = 3 / 4Y, y = 120, so x = 90
1. After the first time: 25-3-1 / 3 = 65 / 3 (m)
After the second time: 65 / 3 × 4 / 5) = 42 / 3 (m)
2. Length x width x height = volume / volume
(L x W + L x H + W x H) = surface area
Set your own formula
three
80 - (7.25 + 8.125) * 5 = 3.125 km

Verification: in a right triangle, 4 times of the sum of squares of the midlines on two right angle sides is equal to 5 times of the square of the hypotenuse. As shown in the figure, let ABC, am and BN be the midlines on BC and AC sides respectively, and AM2 + BN2 = AB2 + Mn2. Verification: 4 (AM2 + BN2) = 5ab2

It is proved that: connecting Mn, the segment Mn is called the median line of △ ABC, Mn ‖ AB and Mn = 12abam2 + BN2 = AB2 + Mn2, so 4 (AM2 + BN2) = 4ab2 + 4mn2. Since m and N are the midpoint of BC and AC, Mn = 12ab. So 4mn2 = AB2.. 4 (AM2 + BN2) = 5ab2