A few math problems of grade one in junior high school· The value of (x + y) ^ 3 (2x + 2Y) ^ 3 (3x + 3Y) ^ 3? 10 ^ α = 20, 10 ^ β = 5 ^ - 1, then the value of 9 ^ α / 3 ^ 2 β is?

A few math problems of grade one in junior high school· The value of (x + y) ^ 3 (2x + 2Y) ^ 3 (3x + 3Y) ^ 3? 10 ^ α = 20, 10 ^ β = 5 ^ - 1, then the value of 9 ^ α / 3 ^ 2 β is?

(x+y)^3(2x+2y)^3(3x+3y)^3=(x+y)^3[2(x+y)]^3[3(x+y)]^3=(x+y)^3*2^3(x+y)^3*3^3(x+y)^3=(2^3*3^3)(x+y)^(3+3+3)=8*27*(x+y)^9=216*(x+y)^910^α=20,10^β=5^-1=1/510^α÷10^β=20÷1/510^(α-β)=10010^(α-β)=1...

For the integer 6X5 + 5X4 + 4x3 + 3x2 + 2x + 2002, given a value of X, if Xiaoying calculates the value of the integer according to the rule of four operations, it needs to calculate 15 times of multiplication and 5 times of addition. Xiaoming said: "there is another algorithm, as long as you add brackets properly, you can keep the number of addition unchanged, while the multiplication only counts 5 times."___ (fill in "right" or "wrong")

The original formula = ({[(6x + 5) x + 4] x + 3} x + 2) x + 2002, the value of 6x is multiplied once, the value of (6x + 5) x is multiplied once, the value of ((6x + 5) x + 4) x is multiplied once, the value of ({[(6x + 5) x + 4] x + 3} x is multiplied once, the value of {[(6x + 5) x + 4] x + 3} x + 2) x is multiplied once, a total of five times

As shown in the figure: two points a and B are on the same side outside the straight line Mn, ab = 5, the distance between a and Mn is AC = 8, the distance between B and Mn is BD = 5, and P moves on the straight line Mn, then the maximum value of | pa-pb | is equal to______ ．

When the point P moves to p ', the | pa-pb | is the largest, | BD = 5, CD = 4, AC = 8, and be ⊥ AC is passed through point B, then be = CD = 4, AE = ac-bd = 8-5 = 3, | AB = AE2 + be2 = 5

Give me a few good books about Mathematical Olympiad!
Or the notes of preparing lessons for the Olympic mathematics
Or introduce a few knowledge about Olympiad Mathematics, the topic is OK

This is a comprehensive topic, not very difficult. In addition, there is Hua Luogeng's mathematics, which seems to be published by Knowledge Publishing House. The "knowledge" printed on the paper usually uses traditional Chinese characters. This set of books is much more difficult than the "Mathematical Olympiad tutorial". The title

What is the integer solution of the equation x + 1 plus x-3 = 4

It is not difficult to know that all integers between - 1 and 3 are solutions of this equation

Junior one under a mathematical problem, find a detailed solution process
Arbitrary quadrilateral ABCD is a piece of paper, how to fold a crease Mn to make Mn / / BC. (upper left corner a, lower left corner B, lower right corner C, upper right corner d) a method has been given: the first fold makes point C coincide with point B to get crease EF; the second fold makes point F coincide with point e to get crease Mn. The reason for finding Mn / / BC (basis)
--Mathematics Evaluation Manual of junior high school

Solution: because of folding, make point C and point B coincide, get crease EF
So EF is perpendicular to BC
Because of the folding, the f-point coincides with the e-point, resulting in the crease Mn
So EF is perpendicular to Mn
So Mn / / BC

Given that 0 ＜ P ＜ 15, P ≤ x ≤ 15. Find the minimum value of X-P + X-15 + x-p-15?

Because P ≤ x, so X-P ≥ 0, so X-P = x-p
Because x ≤ 15, so X-15 ≤ 0, so X-15 = 15-x
Because x-p-15 = x - (P + 15), P + 15 > x, X - (P + 15) < 0,
So x-p-15 = x - (P + 15) = P + 15-x
So the original formula = X-P + 15-x + P + 15-x = 30-x
Because x ≤ 15, when x = 15, the original formula = 30-x = 30-15 = 15

Xiao Li takes three hours to complete the journey. It is known that the downhill road is 15 kilometers faster than the level road per hour, and the uphill road is 25 kilometers slower than the level road per hour?
I don't know how to help you

Xiao Li takes three hours to complete the journey. It is known that the downhill road is 15 kilometers faster than the level road per hour, and the uphill road is 25 kilometers slower than the level road per hour?
The answer is 36

It took more than 30 days for Xuelong to sail from Shanghai to Antarctica at the fastest speed of 19 knots (1 knot = 1 nautical mile / hour). The ship set out from Shanghai at the speed of 16 knots and arrived at its destination several days later. After working in the polar region for several days, it returned at the speed of 12 knots. On the 83rd day after leaving from Shanghai, due to weather reasons, the ship was able to go back to Antarctica The sailing speed is 2 knots. After 2 days, it will continue to sail at the speed of 14 knots and return to Shanghai for 4 days______ Day

Let's use X days to go and work y days, where x is greater than 30. The equation is: 16x = 12 (82-x-y) + 2 × 2 + 14 × 416X = 984-12x-12y + 6028x + 12Y = 10447x + 3Y = 261. It is said above that x must be greater than 30, so only when x = 33, y = 10 and x = 36, y = 3 is in line with the question

The distance between city a and city B is 55 kilometers. Wang Ming started from city a to city B, walked 25 kilometers first, and then changed to riding a bicycle. The speed doubled. When he arrived at city B, he found that the walking time was one hour longer than the cycling time, so the walking speed of Wang Ming was 25 kilometers______ Km / h

Suppose the walking speed is x km / h. 25x-55 − 252x = 1, the solution is x = 10. After testing, x = 10 is the solution of the original equation. A: the walking speed is 10 km / h