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Compare size (1) Compare size ①1²＋5² ﹙﹚ 2×1×5 ②﹙－2﹚²＋3² ﹙﹚ 2×﹙－2﹚×3 ③（－4）²＋﹙－4﹚² ﹙﹚ 2×（－4﹚×（－4﹚ (2) Follow the example of ①, ② and ③ in (1) to write a formula respectively; (3) What regular conclusion do you find through observation, conjecture, exploration and induction? Please try to explain this regular conclusion
①＞ ②＞ ③＝
2²+4²＞2×2×4
（-5）²+9²＞2×（-5）×9
（-6）²+（-6）²＝2×（-6）×（-6）
The sum of the squares of two different numbers is more than twice the product of the two numbers
The sum of the squares of two identical numbers is equal to the product of the two numbers
The process of solving mathematical problems in detail
21lg20/3-lg7+21lg3+lg7/4
（lg5）^2+lg2*lg5+lg2
1. The original formula is 21 (LG20 / 3 + Lg3) - lg7 + lg7 - LG4
=21lg20-2lg2
=21(2lg2+lg5)-2lg2
=21(lg2+lg5)+21lg2-2lg2
=21+19lg2
2. The original formula is lg5 (lg5 + LG2) + LG2
=lg5+lg2
=1
Please help to solve some math problems (need more detailed process)
1. Given the vertex a (3, - 1) of the triangle ABC, the linear equation of the central line on the side AB is 6x + 10y-59 = 0, and the linear equation of the bisector of angle B is x-4y + 10 = 0, the equation of the line on the side BC is obtained
2. Suppose that the chord length obtained by cutting Y-axis is 2; it is divided into two arcs by x-axis, and the ratio of arc length is 3:1; the distance from the center of the circle to the straight line L: x-2y = 0 is 5 / 5, then the equation of the circle is solved
3. Let m be the moving point on the circle X2 (square) + y2-6x-8y = 0. O be the origin and n be the point on the ray OM. If loml (absolute value) xlonl = 0, the trajectory equation of point n is obtained
4. There is only one circle which has known a (0,1) and B (4, a) and is tangent to the x-axis. Find the value of a and the equation of the circle
5. The real coefficient equation f (x) = x2 + ax + 2B = 0 has one root in (0,1) and the other root in (1,2)
(1) : B-2 / A-1
(2) : (A-1) 2 (for square) + (b-2) 2
(3) The range of: a + B-3
I'm just a freshman. It's hard
RELATED INFORMATIONS
- 1. Three students have done a total of 20 math problems. If B does one more problem, it will be twice as many as a. if a does five less problems than C, how many math problems did each of the three students do
- 2. One day, a, B and C do math problems. It is known that a has done 6 more than B, and C has done 2 times as much as a, 22 more than B, so they have done all of them______ A math problem
- 3. Ask a math question about comparing size It is known that the quadratic function f (x) satisfies f (- x + 2) = f (- 2-x). Compare the sizes of F (negative half root sign 3), f (negative third π) and f (- 1)
- 4. Compare the size 10X3/8（ ）10 4X3/4（ ）4 3/8X10（ ）3/8 4/3X4（ ）4/3
- 5. What is the common multiple of 8 and 9 within 50?
- 6. 1 2 3 4 56 7 8 9 10 11 12 13 14 15.......... 96 97 98 99 100 a B 1. Frame out the four numbers C D from the middle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ............... 96 97 98 99 100 a b 1. Frame out the four numbers C and D, set the minimum number as X, and express the sum of the four numbers with integral a 2. Box out the five numbers B, C and D, and let the number in the middle be y, If their sum is equal to 85, write these five digits
- 7. 2/1+6/5—12/7+20/9—30/11+42/13—56/15
- 8. Two thirds of the students in class 1 of grade 6 subscribe to primary school students' mathematics newspaper, and three quarters subscribe to mathematics PHS At least ()
- 9. Sixth grade mathematics volume I exercise book page 34 question 4 people's Education Press
- 10. The correct one in the following statement is () A. A positive number and a negative number are opposite to each other B. the opposite number of any number is different from itself C. any number has its opposite number D. the numbers represented by two points on both sides of the origin on the number axis are opposite to each other
- 11. Compare the sizes of 222221 / 222223 and 333331 / 333334
- 12. Compare the size of - 8 / 9 and - 7 / 9
- 13. A preliminary mathematical problem In solving the equations ax + by = C (1), ax by = - 3 (2), due to carelessness, Xiao Ming mistook - 3 in equation (2) as 3, and got the solution as x = 3, y = 6. Xiao Gang mistook the value of B in equation (1), and got the solution as x = 15, y = 18. It is known that neither of them made any other mistakes. Try to find the value of a, B, C
- 14. Let's do it for you, 1: For a project, if it is contracted by Party A and Party B and completed in 12 / 5 days, it needs to pay 180000 yuan; if it is contracted by Party B and Party C and completed in 15 / 4 days, it needs to pay 150000 yuan; if it is contracted by Party A and Party C and completed in 20 / 7, it needs to pay 160000 yuan. Now the project is contracted by a single team. On the premise that the project can be completed in one week, which team has less contract cost? 2: When a shopping mall sells a commodity, its profit margin increases by 8 percentage points because the purchase price is 6.4% lower than the original price. Then the original profit margin of this commodity is... (Note: profit margin = (sales price purchase price) X100%. I can't understand the first floor product.) (just these two questions, 50 points.) 3: The number of integer solutions (x, y) of the equation x & sup2; + XY + 2Y & sup2; = 29 is () A.2 B.3 C.4 D. infinite
- 15. 2*4/1+6*8/1+… +2006*2008/1+4*6/1+8*10/1+… What is 2004 * 2006 / 1
- 16. The solution set of inequality 2 Λ X - (3 / x) + 1 ≤ 1 / 2 is 2∧[x－﹙3／x﹚＋1]≤1／2
- 17. What is (x ^ n-1) ^ 2 (- 3 ^ 3) (- x ^ n) equal to?
- 18. Choose + - x division or bracket to write 1,2,7,9 into a formula, the result is 24, the formula is?
- 19. 1 2 3 4 5 6 7 8 9 10 = 2014 with addition, subtraction, multiplication, division of brackets, etc. without changing the numerical order, it is equal to 2014
- 20. Six out of seven / five out of nine * equals seven out of eight