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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
A:
Let X be the absolute value of | a | / (B + C) + B / (c + a) + C / (a + b)
So:
x=| |a|/(-a)+|b|/(-b)+|c|/(-c)| |
1) If a is positive, B and C are negative
x=|-1+1+1|=1
2) If a and B are positive, C is negative
x=|-1-1+1|=|-1 |=1
To sum up, x = 1
So:
x^19-99x+2002
=1-99+2002
=2004-100
=1994
Given that a and B are rational numbers, compare the size of (a + b) and (a-b),
b> The former is greater than the latter
b
Given that a and B are positive rational numbers, let m = B / A, n = 2A + B / A + B, compare the size of M and n
Would you like to discuss the size of b square and 2A square?
[would you like to discuss the size of square B and square 2A
It can be said that, in fact, it is to discuss the proportional relationship between a and B
m=b/a
n=(2a+b)/(a+b)
m-n=b/a-(2a+b)/(a+b)=[b(a+b)-a(2a+b)]/[a(a+b)]
=(ab+b^2-2a^2-ab)/[a(a+b)]
=(b^2-2a^2)/[a(a+b)]
When B ＞ (radical 2) a, m ＞ n
When B = (radical 2) a, M = n
When B ＜ (radical 2) a, m ＜ n
Given that the parabola and X-axis intersect at points m (- 1,0) and n (2,0) and pass through points (1,2), find the expression of this function
Solution 1: substituting (- 1, 0), (2, 0), (1, 2) into y = AX2 + BX + C, we get a − B + C = 04A + 2B + C = 0A + B + C = 2, we get a = − 1b = 1C = 2, the expression of this function is y = - x2 + X + 2; solution 2: let the analytic expression of the function be y = a (x + 1) (X-2), substituting (1, 2) into y = - (x + 1) (X-2), that is y = - x2 + x + 2
Find the value of 1 / (x + 4) - 1 / (x + 7) = 1 / (x + 3) - 1 / (x + 6)
1/(x+3)-1/(x+4)=1/(x+6)-1/(x+7)
(x+6)(x+7)=(x+3)(x+4)
6x=-30
x=-5
The negative - x + 2Y is 3x-y, which does not change the value of the fraction, so that the first term of the molecule is positive, and the fraction itself does not have a "-" sign
Negative - x + 2Y / 3x-y
=3x-y of x-2y
Solving one variable quadratic equation 2x-2x2-2 / 1 ≥ 0
2x-2x & # 178; - 1 / 2 ≥ 0 is an equation or an inequality? 4x & # 178; - 4x + 1 ≤ 0 (2x-1) & # 178; ≤ 02x-1 = 0x = 1 / 2, so the solution of the original inequality is x = 1 / 2, the solution of the quadratic equation with one variable is 2x-2x2-2 / 1 = 04x & # 178; - 4x + 1 = 0 (2x-1) & # 178; = 02x-1 = 0x = 1 / 2, so the solution of the quadratic equation with one variable is x = 1 / 2
Fraction calculation: 1. (4 / m ^ 2-4) - (1 / m-2) 2. X + Y - (x ^ 2 + y ^ 2 / x + y) 3. 1 - (x multiplied by 1 / 1-x)
(4/m^2-4)-(1/m-2)
=4/(m+2)(m-2) -1/(m-2)
=4/(m+2)(m-2)-(m+2)/(m+2)(m-2)
=(4-m-2)/(m+2)(m-2)
=(2-m)/(m+2)(m-2)
=-1/(m+2)
2.x+y-(x^2+y^2/x+y)
=(x+y)²/(x+y)-(x²+y²)/(x+y)
=[(x+y)²-x²-y²]/(x+y)
=2xy/(x+y)
3.1 - (x multiplied by 1 / 1-x)
=1+x/(x-1)
=(x-1+x)/(x-1)
=(2x-1)/(x-1)
4(x+2)=1-5x 3(y+2)=3-2 y/2+x/3=13 y/3-x/4=3 x+y=420 30%x+40%y=160*180% 2x-1/5+3y-2/4=2 3x+1/3-3y+2/
4(x+2)=1-5x
3(y+2)=3-2
y/2+x/3=13
y/3-x/4=3
x+y=420
30%x+40%y=160*180%
2x-1/5+3y-2/4=2
3x+1/3-3y+2/4=4/3
x/2+y/3=2
2x+3y=28
4X + 8 = 1-5x (4 + 5) x = 1-8x = - 7 / 93y = 1-6y = - 5 / 3; Y / 2 = 13-x / 3Y = 26-2x / 3 (26-2x / 3) / 3-x / 4 = 3 - (2 / 9 + 1 / 4) x = 3-26 / 3x = 12Y = 26-24 / 3 = 18; y = 420-x0.3x + 0.4 (420-x) = 160 * 1.8-0.1x = 120x = - 1200y = 1620; by simplification, 2x + 3Y = 2.7 X-Y = 1 / 6x = y + 1 / 62 (y + 1
Use the reduced order method to calculate the following determinants
(1) r1-r2
Then c2-c1
Determinant into
x 0 0 0
1 -x 1 1
1 0 1+y 1
1 0 1 1-y
Expand by line 1 (reduced)
Then expand by column 1
(3)
Expand d = x * x ^ (n-1) + (- 1) ^ (n + 1) y * y ^ (n-1) = x ^ n + (- 1) ^ (n + 1) y ^ n by column 1
RELATED INFORMATIONS
- 1. It is known that a and B are rational numbers, and a > 0, B
- 2. (1) If two rational numbers a and B satisfy the relation (A-1) (B-1)
- 3. If there are two rational numbers a and B satisfying (A-1) (B-1) > 0, what is the relationship between them and 1?
- 4. a. B is two arbitrary rational numbers. Compare the size of a + B and B
- 5. A. B is any rational number, try to compare the size of a + B and a-b
- 6. If a and B satisfy a + B = 3 and A-B = 2, then A-B = ()
- 7. If the rational numbers a and B satisfy (a + 2) √ 2 = B-3, then a ∧ B A ∧ B is the power B of A
- 8. 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
- 9. 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|
- 10. 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
- 11. 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
- 12. 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
- 13. If (a-b) / (a + b) is not equal to 1, it is proved that a / B is a rational number
- 14. 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)
- 15. 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
- 16. 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
- 17. 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?
- 18. 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)
- 19. Look at the following column of numbers to find out the law: minus half, two thirds, three quarters, four fifths, six fifths, seven sixths Write the number of items 7, 8 and 9 What is the number 2014? Question (3) if this column of numbers is arranged infinitely, which two numbers are closer to each other?
- 20. The outline of composition in unit 8 of Volume 1 of grade 5 is below 150