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(1) If two rational numbers a and B satisfy the relation (A-1) (B-1)
(1) Can judge, according to the positive and negative get negative get:
a-1>0
b-11,b
If two rational numbers a and B satisfy a ＞ 0, B ＜ 0, a ＜ B, then ()
A、—a〈b〈a〈—b
B、b〈—a〈a〈—b
C、—a〈—b〈b〈a
D、b〈 —a〈—b〈b
a〉0,b〈0,｜a｜〈｜b｜
So a B
=a
Addition and subtraction of fractions: 2x ^ 2-5x-2 + 3 / (x ^ 2 + 1)
2x^2-5x-2+3/(x^2+1)
＝(x^2+1)(2x^2-5x-2)/(x^2+1)+3/(x^2+1)
＝(2x^4－5x^3-5x+1)/(x^2+1)
(is the title wrong? There's no way to simplify it.)
Jiangsu Wu Yunchao wish you progress in your study!
Abacus usage
Explain the meaning of those pithy formulas. I can't understand them after reading them for a long time Explain with examples~
There are four types of formula for abacus addition: one (a few up a few) for example: two up two means to add two directly, for example, one up two, first dial one up, add two directly dial two up, because this file does not rely on the number of beams, the next file has enough two, it is equal to three
78 times 98, simple algorithm
An is a sequence of arithmetic numbers, and find &; LIM (Sn + Sn + 1) / (Sn + sn-1)
lim (Sn+Sn+1)/(Sn+Sn-1)
=[n(n+1)/2+(n+1)(n+2)/2]/[n(n+1)/2+n(n-1)/2]
=(2n²+4n+2)/2n²
=1+2/n+1/n²
I just want to know what the first step is
an=n
sn=n(n+1)/2
Inequality
Let the absolute values of a, B and C be less than 1, and prove that BC + Ca + AB + 1 > 0
Let the absolute values of a, B and C be less than 1, and prove that BC + Ca + AB + 1 > 0
It is proved that f (x) = (B + C) x + BC + 1, ︱ x ︱ 0 is constructed as a function of degree
To prove 2cos ^ 2A + sin ^ 4A = cos ^ 4A + 1
It is proved that: (COSA) ^ 4 + 1 - (Sina) ^ 4 = (COSA) ^ 4 + (Sina) ^ 2 + (COSA) ^ 2 + (Sina) ^ 2 = [(COSA) ^ 2 + (Sina) ^ 2] + (Sina) ^ 2 + (COSA) ^ 2 = (COSA) ^ 2 - (Sina) ^ 2 + (COSA) ^ 2 = 2 (cos
Approximate solution of equation x = 5-E ^ X in (1,2) by dichotomy
5-E ^ x-x let x take 1 and 1.5 first to get Y1;
Let x take 2 and subtract 1.5 to get Y2;
Judge the small value of Y1 and Y2, if Y1 is small, then take a pair of 1 and 1.25 and a pair of 1.25 and 1.5, and continue to go straight, the y value obtained is smaller than the expected value, and then take the median value to meet the requirements
How to take the free variable in the basic solution system in linear algebra? It is the main way to find the unknown in linear algebra later, or to find the eigenvector. I don't know how to determine the free variable
Which is x1, X2, X3
Aligned sublinear equations AX = 0
Transform coefficient matrix A into ladder matrix with elementary row
(in this case, the free variables can be determined, but it is better to be reduced to the row simplest form for the convenience of solution)
The variables corresponding to the first nonzero element in the nonzero row are constraint variables, and the rest are free variables
(this is the best way to master, and you don't have to worry about other ways.)
RELATED INFORMATIONS
- 1. If there are two rational numbers a and B satisfying (A-1) (B-1) > 0, what is the relationship between them and 1?
- 2. a. B is two arbitrary rational numbers. Compare the size of a + B and B
- 3. A. B is any rational number, try to compare the size of a + B and a-b
- 4. If a and B satisfy a + B = 3 and A-B = 2, then A-B = ()
- 5. If the rational numbers a and B satisfy (a + 2) √ 2 = B-3, then a ∧ B A ∧ B is the power B of A
- 6. If a and B are rational numbers and | a | + | B | = 0, then () A. A and B are opposite numbers, B. A = b = 0C. A and B have opposite signs, and the value of d. A and B does not exist
- 7. Mathematical problems know that a and B are rational numbers, a > 0, B < 0. Simplify | B | - | a | + | A-B | + | a + B| It is known that a and B are rational numbers, a > 0, B < 0. Simplify | B | - | a | + | A-B | + | a + B|
- 8. If the rational numbers a and B satisfy | ab-2 | + | 1-B | = 0, Let's try to find one of ab ＋ (a ＋ 1) (B ＋ 1) ＋ (a ＋ 2) (B ＋ 2) ＋ ＋﹙a＋2011）﹙b＋2011 A value of 1 / 2
- 9. It is known that a, B and C are nonzero rational numbers It is known that a, B and C are nonzero rational numbers The molecules are a + B + C + BC + AC + AB + ABC. These are molecules; The denominator is the absolute value of the numerator above Simplify them. The sign is the plus sign By 9:30 tonight, urgent! Before 10:00 The process should be clear and easy to understand!
- 10. Given proposition p: x > 0, proposition q: x square > 0, then p is a, B and C of Q, and a + b > C is a, B and V Given the proposition p: x > 0 and the proposition q: x square > 0, then p is Q a. If B and C are three line segments, then a + b > C is that a, B and V can form a triangle Li Min is an 18-year-old college student
- 11. It is known that a and B are rational numbers, and a > 0, B
- 12. Let x = the absolute value of a / (B + C) + B / (c + a) + C A + B, let ABC not be 0, and a + B + C = 0 The 19th power of x-99x + 2002
- 13. Rational number: 1. The following statement is wrong: () A all rational numbers can be represented by points on the number axis The origin on the b-axis represents the number 0 The point of number - A on the c axis is to the left of the origin D 0 is the dividing point between positive and negative numbers 2. On the number axis, the following statement is incorrect: () A two rational numbers, the absolute value of large far from the origin B two rational numbers, the big one is on the right side of the number axis C two negative rational numbers, the big one is near the origin D two rational numbers, the big one is far from the origin 3. The following statement is correct: () A positive and negative numbers are called rational numbers B integers and fractions are called rational numbers C positive and negative integers are collectively called integers D fractions include fractions and negative decimals 4. The following statement is correct: () ① The absolute values of two opposite numbers are equal ② The absolute value of both positive and zero equals itself ③ Only the absolute value of a negative number is its opposite ④ The opposite absolute value of a number must be negative A. 1 B, 2 C, 3 D, 4 d
- 14. If a is a rational number, then the sum of - A and | a | is () A may be plural B is not plural C can only be positive D can only be 0 E is not a positive number F can't be sure
- 15. If (a-b) / (a + b) is not equal to 1, it is proved that a / B is a rational number
- 16. A is a rational number which is not equal to 0. Try to compare the size of a with 1 / a (hint: discuss the classification of a)
- 17. If a, B and C are rational numbers that are not equal to 0, what is the result of a / [a] + B / [b] + C / [C]? None
- 18. a. Both B and C denote rational numbers which are not equal to 0, and satisfy the following conditions: a + | B + | B + | C| 1) Try to judge the sign of a, B and C (2) Find the value of | ABC | in the formula ABC
- 19. If the distance between the point of number a and the origin on the number axis is 2, what is the sum of the absolute values of a + negative a?
- 20. 1. Negative integers with absolute values greater than 1 and less than 3 are____ ; the largest negative integer is_____ The number with the smallest absolute value is______ 2. If | - a | - a = 0, then a is_____ Ab | ab | = - 1 (b)