The inequality x ^ 2 + 2aX + a > 0 holds for X ∈ (1,2] to find the range of A x∈[1,2)

The inequality x ^ 2 + 2aX + a > 0 holds for X ∈ (1,2] to find the range of A x∈[1,2)

According to the meaning of the title:
4+4a+a>0
(2a)²-4a＜0
That is 0 < a < 1

When x > 0, the inequality x ^ 2 + 2aX + A ^ 2 - (1 / 2) a - (3 / 2) > 0 holds, and the value range of a is obtained

x^2+2ax+a^2-（1/2）a-(3/2)=(x+a)^2-a/2-3/2
1) A0 a = 0, a ^ 2-A / 2-3 / 2 > 0 A3 / 2, so a > 3 / 2
To sum up, A3 / 2

How can refrigerators turn electricity into energy
Some say it's thermal energy, some say it's mechanical energy

98% of the energy is converted into mechanical energy and 2% into heat and other forms of energy

One part of X + y and one part of X-Y,

1/(x+y)=(x-y)/(x²-y²
1/(x-y)=(x+y)/(x²-y²

If the lamps L1 and L2 marked with "220V 25W" and "220V 60W" are connected in series in the circuit with voltage of 220V, the power ratio of L1 to L2 is

Because two resistors are connected in series, the current is equal. According to the formula power = the square of current multiplied by resistance, we can know that the power ratio of L1 and L2 is equal to the resistance ratio of the two. For lamps marked with "220 V 25 W" and "220 V 60 W", we can calculate the resistance respectively. According to the formula power = the square of voltage divided by resistance, we can get R1 = 220 ^ 2

If the expansion of (x2 + mx-8) (x2-3x + n) does not contain terms x2 and X3, the values of M and N are obtained

The original formula is X4 + (M-3) X3 + (n-3m-8) x2 + (Mn + 24) x-8n. According to the expansion without x2 and X3 terms, m − 3 = 0n − 3M − 8 = 0, the solution is m = 3N = 17

Known motor 15kw, how to calculate the cross-sectional area of wire and cable? Find a simple formula

15kw 3-phase motor rated current 30A
Generally, the copper conductor can bear 8A current if it is 1 square millimeter. If it is more than 20 meters, it can be counted as 6A if it is 1 square millimeter
The formula is very complex, depending on the material of your wire, single strand or multi strand

In the triangle ABC, angle c is 90 degrees, AB is 5, and its circumference is 12. Find the radius of its inscribed circle
Why is radius calculated by dividing area by perimeter

Using Pythagorean theorem, we can find that the two right sides of a triangle are 3 and 4 respectively
Then the radius of the inscribed circle can be obtained by the area method
The radius is 3 * 4 / 12 = 1
How to solve the problem:
Connect the center of the circle and the three vertices of the triangle. Three equal height triangles are obtained. The height is the radius of the circle. Therefore, the sum of the areas of the three triangles is the radius * 12 / 2
The area of the original triangle is 3 * 4 / 2
So the radius is 3 * 4 / 12 = 1
Do you understand?

The watt hour meter is marked with 3000r / kWh. If a single consumer with 60W power is used, the number of revolutions of the turntable of the watt hour meter in 100s is ()

The revolution of 100s is 5. The formula is the same as that of upstairs, but the answer is wrong. Only 5 revolutions is not 50

(A-2) & #178; - 6 (2-A), where a = - 2 decomposes the factor first, and then calculates and evaluates

﹙a－2﹚²－6﹙2－a﹚
＝﹙a－2﹚²＋6﹙a－2﹚
＝﹙a－2﹚﹙a＋4﹚
When a = - 2,
The original formula = (- 2-2) × (- 2 + 4) = - 8