The range of finding x with the power of X & # 178; + X + 3 of a > 2x & # 178; - 2x-1 of a

The range of finding x with the power of X & # 178; + X + 3 of a > 2x & # 178; - 2x-1 of a

a^(x²+x+3)>a^(2x²-2x-1) a>0 a≠1
When a > 1, X & # 178; + X + 3 > 2x & # 178; - 2x-1, X & # 178; - 3x-4

Let x = 1, then the 12th power of a12x + the 11th power of a11x + +The second power of a2x + a1x + A0 = A12 + a11 + A10 + +A2 + A1 + A0, so A12 + a11 + A10+
Let x = 1
Then the 12th power of a12x + the 11th power of a11x + +The second power of a2x + a1x + A0 = A12 + a11 + A10 + +A2+A1+A0
So A12 + a11 + A10 + +A2+A1+A0=(1²-1+1)^6=1
Let x = - 1
Then the 12th power of a12x + the 11th power of a11x + +The second power of a2x + a1x + A0
=A12-A11+A10-…… +A2-A1+A0
So a12-a11 + a10 - +A2-A1+A0
=[(-1)²-(-1)+1]^6
=729
And A12 + a11 + A10 + +A2 + A1 + A0 = (1 & # 178; - 1 + 1) ^ 6 = 1
2(A12+A10+A8+A6+A4+A2+A0)=730
2 (A12 + A10 + A8 + A6 + A4 + A2 + A0) = 730

Before this, there should be a premise: ∑ I = 0to12 (AIX ^ I) = (x ^ 2-x + 1) ^ 6 is hidden by you? Because this is: when x = 1 ∑ [a string of summation] = A12 + a11 +. + A2 + A1 + A0 (= 1) [∵ 1 ^ 6 = 1] when x = - 1 ∑ = a12-a11 +. + a2-a1 + A0 (= 729) [∵ 3 ^ 6 = 729] when x = 1

It is known that the fifth power of (x + 1) = the fifth power of a0x + the fourth power of a1x + the third power of a2x + the second power of a3x + a4x + A5. ① find the value of A0 + A1 + A2 + a3 + A4 + A5
② Find the value of a1 + a3 + A5

(1) Let x = 1, we get: A0 + A1 + A2 + a3 + A4 + A5 = 2 ^ 5 = 32
(2) Let x = - 1, we get: - A0 + a1-a2 + a3-a4 + A5 = 0
By adding to (1), we get 2 (a1 + a3 + A5) = 32, so: a1 + a3 + A5 = 16

As shown in the figure, △ ABC is an equilateral triangle, points D and E are on AB and BC respectively, ad = be, AE and CD intersect F, indicating that ∠ BAE = ∠ ACD

This is a problem of similar triangles
In equilateral triangle ABC, it can be concluded that ad is equal to be, angle Abe is equal to angle CAD, and edge AB is equal to ac. these three conditions can prove that triangle Abe is similar to triangle CAD, and angle Bae is equal to ACD

The square of X is 17, so how much is x?
Is it ± root 17 or ± 17?

The root number is 17

A trapezoid has an area of 240 square centimeters and a height of 15 centimeters. The ratio of the upper bottom to the lower bottom is 3:5. The upper bottom of this trapezoid is () centimeters and the lower bottom is () centimeters（

240×2÷15÷(3+5)
＝480÷15÷8
＝32÷8
= 4cm
Upper bottom: 4 × 3 = 12 cm
Bottom: 4 × 5 = 20 cm

As shown in the figure, △ ABC and △ ade are symmetric with respect to the straight line Mn. The intersection F of BC and De is on the straight line Mn. ① point out the symmetrical points in two triangles; ② point out the equal line segments and angles in the figure; ③ is there any symmetrical triangle in the figure?

① A → a, B → D, C → e, ② AB = ad, AC = AE, BC = De, ∠ BAC = ∠ DAE, ∠ B = ∠ D, ∠ C = ∠ E. ③ without additional letters and line segments, △ AFC and △ AFE, △ ABF and △ ADF are also axisymmetric with respect to the straight line Mn

Using the collocation method to solve the equation x squared plus 10x plus 1 is equal to 60

X ^ 2 + 10x + 1 = 60 x ^ 2 + 10x + 25 = 84 (x + 5) ^ 2 = 84 x + 5 = ± 2 √ 21 x = 5 + 2 √ 21 or 5-2 √ 21

The relationship between the moon, the earth, the sun and the stars. The magical universe
The moon, the earth, the sun, the stars, the magic universe
I want to ask why the moon looks the same size as the sun in the sky. It looks the same size in the sky. I know it's the relationship between volume and distance, but so many stars in the sky look the same size, so there is no one half the size of the moon in the sky, No one is only half the size of the moon or the sun, and the sun and the moon look the same size in the sky. Is there such a clever distance and volume? What's this? Is there any connection between them
The moon and the sun so coincidentally. There is no half moon big star!

This is the problem of proportional calculation
For example, if you look at a sphere with a diameter of 10 meters at a distance of 10 meters, its apparent diameter is 60 degrees. If you look at a sphere with a diameter of 100 meters at a distance of 100 meters, its apparent diameter is 60 degrees. The former can just cover the latter
In fact, the moon, the sun and the earth have the same relationship,
After many years of evolution, today's sky, the moon can just cover the sun, because the distance between the sun and the earth is 400 times that of the moon, and the diameter of the sun is just 400 times that of the moon. On the earth, the moon can completely cover the sun. As for this total solar eclipse, the apparent diameter of the moon is 33 minutes 31 seconds, the apparent diameter of the sun is 31 minutes 27 seconds, and the eclipse minute is 1.08
In fact, the moon is far away from the earth within 2 miles a year. In the age of dinosaurs, the moon was much larger than today. At that time, the total solar eclipse could last for more than ten minutes, and there was no annular eclipse (because the apogee of the moon could cover the sun). But in another billion years, when the moon could not cover the sun at the perigee, we would never see the total solar eclipse, only the annular eclipse
As for why there are no stars half the size of the moon, it is because the radius of the planets in the solar system is too small, and the apparent diameter is only a few tenths of a second. The constancy outside the solar system is too far away from the earth, and the nearest one is dozens of light years. No matter how big it is, we look very small. This is also the reason why only one hand covers the sky

Do you have any math problems in the sixth grade volume 2 of Beijing Normal University Edition!

1. Make a round iron bucket without cover, with a height of 20 DM and a bottom diameter of 12 DM. How many square meters of iron can be used to make the water? 2. Cut a cylinder into two identical cylinders with a bottom radius of 3 cm. How much is the surface area added? 3. Cut the cylinder into two halves with a bottom diameter of 10 cm. The surface area is increased by 40