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I'm a sophomore in high school, what do you want to ask?
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Summary. Who will do the math of the second year of junior high school.
Hello dear. You can send the question to see.
2,3 How to do it with functions without geometry.
It's a little hard to see the picture.
Wait a minute. You want to do it with a function.
Yes, yes, you don't need geometry, the second question is OK, how to say that the value is constant, and then how to find it.
Yes, yes, you don't need geometry, the second question is OK, how to say that the value is constant, and then how to find it.
Set the coordinates of point b.
c' is in a straight line x+y=4, so the angle does not change.
Understood?
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1.∵x²+x-1=0
x²=1-x, x²+x=1
x³-2x+2008
x*x²-2x+2008
x*(1-x)-2x+2008
x-x²-2x+2008
(x²+x)+2008
2.The polynomial x -2x +ax+b divides (x -x-2) to give the remainder of 2x+1
kx+m)(x -x-2)+(2x+1)=(x -2x +ax+b) (k, m are integers).
kx³-kx²-2kx+mx²-mx-2m+2x+1=x³-2x²+ax+b
kx³+(m-k)x²+(2-2k-m)x+1-2m=x³-2x²+ax+b
k=1, m-k=-2, a=2-2k-m ,b=1-2m
k=1, m=-1, a=1, b=3
a/b =1/3
4.(ab+1+a-b)(ab+1-a+b)
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The first way is to find x with the universal formula and then bring in the solution.
Factorization. Less than, factorization.
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Solution: 1
x^2+x-1=0
x^3-2x+2008
x^3+x^2-x-x^2-x+1+2007=x(x^2+x-1)-(x^2+x-1)+2007=0+0+2007
2. That is, x 3-2x 2+ax+b-(2x+1) is divisible by (x 2-x-2).
x^3-2x^2+ax+b-2x-1
x^3-2x^2+(a-2)x+(b-1)=x^3-x^2-2x-x^2+ax+b-1=x(x^2-x-2)-(x^2-ax-b+1)a=1 -b+1=-2
The solution yields a=1 b=3
a/b=1/3
4. It's okay to decompose it to this step, and you don't need to divide it anymore.
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First of all, you have to like mathematics, understand the basics, and you will naturally be able to do problems, and you have to memorize more formulas. If you are not annoyed, you can preview what you will go on later, try to retrace some formulas and theorems by yourself, this is a compulsory course for mathematical methods, such as x 0sin(x) x 1 It is necessary to push it down, and the Lagrange median theorem and so on and many other things. Anyway, when I was studying high math, I reasoned.
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1. The homework must be done by yourself, so that you will concentrate in class, and you will not be very eager for the teacher's explanation
2.Don't rush to take notes when the teacher talks about the topic, just understand it, even if you think you have understood, when you do it again after class, you will find that you have no idea, because it is the teacher's idea that you have not yet absorbed.
3.You have to do a proper set of wrong questions, because if you don't solve a similar problem, you will make a mistake when you encounter one, in the wrong set you have to write down the idea of doing this question, why you will not do it right, don't repeat the similar question type, I memorized more than a dozen wrong question sets in high school, and I didn't have time to read it during the college entrance examination.
4.The formula must be familiar, even if you can't memorize the concept, but you must be able to use it, which is very important, when you see a problem, you have to know what formula to use.
5.If you can't do it yourself, don't keep holding on to it, ask your classmates or teachers, this method is better, if you are in high school, you don't have that much time to drill.
That's just my opinion, I hope it helps you.
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The nature of Yang Hui's triangle:
1.Each number is equal to the sum of the two numbers above it.
2.The numbers in each row are symmetrical and gradually increase in size starting from 1.
3.The number in line n has n terms.
4.The sum of digits in line nth is 2n-1.
5.The number of m in row n can be expressed as c(n-1,m-1), which is the number of combinations of m-1 elements from n-1 different elements.
6.The mth number of the nth row and the n-m+1 number are equal, which is one of the properties of the combined number.
7.Each number is equal to the sum of the left and right digits of the previous row. The entire Yang Hui Triangle can be written with this property.
That is, the ith number of the n+1 row is equal to the sum of the i-1 number and the ith number of the nth row, which is also one of the properties of the combined number. i.e. c(n+1,i)=c(n,i)+c(n,i-1).
8.The coefficients in the equation (a+b)n correspond to each of the terms in row (n+1) of Yang Hui's triangle.
9....... the first number from line 2n+1 with the third number from line 2n+2 and the fifth number from line 2n+3In a line, the sum of these numbers is the 4n+1 Fibonacci number; ...... the second number (n>1) from line 2n with the fourth number from line 2n-1 and the sixth number from line 2n-2The sum of these numbers is the 4n-2nd Fibonacci number.
10.Arrange the numbers in each row to obtain the n-1 (n is the number of rows) power of 11: 1=11 0; 11=11^1; 121=11^2……When n>5 would not be in line with this property, the rightmost number of the nth line should be used"1"Place in the single digit, and then align the single digit of a number on the left to the ten.
..And so on, fill in the empty space with "0", and then add up all the numbers, and the number obtained is exactly 11 to the n-1 power. Taking n=11 as an example, the number in row 11 is:
1,10,45,120,210,252,210,120,45,10,1, the result is 25937424601=1110.
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