X2-3x + 2 = 10 find the square of X1 + the sum of squares of x2 1 / 2 + 1 / 2

X2-3x + 2 = 10 find the square of X1 + the sum of squares of x2 1 / 2 + 1 / 2

∵X^2-3X+2=10
X^2-3X-8=0
∴x1*x2=-8,x1+x2=3
x1^2+x2^2=(x1+x2)^2-2x1x2=3^2-2(-8)=9+16=25
1/x1+1/x2=(x1+x2)/(x1*x2)=3/(-8)=-3/8
A series of problems to find the formula of general term
In the sequence {an}, if A1 = 2, a (n + 1) = 2An / a (n) + 1, then the general term formula of the sequence {an} is
N + 1 on the left side of the equation is the subscript, and on the denominator on the right side is the an + 1
A (n + 1) = 2An / an + 1 (n + 1) denotes the reciprocal on both sides of the subscript
1/a(n+1)=(an+1)/2an
1/a(n+1)=1/2an+1/2
1/a(n+1)-1=(1/2)(an-1)
[1/a(n+1)-1]/(1/an-1)=1/2
So {1 / an-1} is an equal ratio sequence with 1 / A1-1 = - 1 / 2 as prime minister and q = 1 / 2 as common ratio
1/an-1=(-1/2)(1/2)^(n-1)=-(1/2)^n
1/an=1-1/2^n
So an = 2 ^ n / (2 ^ n-1)
Take the reciprocal
1/a(n+1)=(an+1)/2an=1/2+1/(2an)
Let BN = 1 / an
Then B (n + 1) = 1 / 2 + 1 / 2 * BN
b(n+1)-1=1/2*bn-1/2=1/2*(bn-1)
So bn-1 is an equal ratio sequence
q=1/2
b1=1/a1=1/2
So bn-1 = 1 / 2 * (1 / 2) ^ (n-1) = (1 / 2) ^ n
So BN = 1 + (1 / 2) ^ n
So an = 1 / BN = 1 / [1 + (1 / 2) ^ n]
The sum of solutions of the common equation is y = M-3, y = M-9
By substituting x = 3, y = - 1 into the equation 4x + my = 9 and MX NY = 11, we get the following results:
12-m=9
3m+n=11
Get:
M=3
N=2
Let X1 and X2 be the two heels of the equation 2x-5x-1 = 0, and find 1 / 1 of X1 and 1 / 2 of x2
2X square - 5x-1 = 0x square - 5 / 2x-1 / 2 = 0x square - 5 / 2x = 1 / 2x square - 5 / 2x + 5 / 4 square = 1 / 2 + 5 / 4 square (X-5 / 4) square = 33 / 16x-5 / 4 = positive and negative root sign 33 / 4x = positive and negative root sign 33 / 4 + 5 / 4x1 = root sign 33 / 4 + 5 / 4x2 = negative root sign 33 / 4 + 5 / 4x1 / 1 = (- 5 + root sign 33) / 2x2 / 1 = (- 5
How to find the general term formula in the sequence problem
In known sequence an, A1 = 0, a (n + 1) = an + 2N-1. The general term formula of an
a1=0,a(n+1)=an+2n-1
When n = 1
a2=a1+2-1=1
When n = 2
a3=a2+4-1=4
When n = 3
a4=a3+5=9
When n = 4
a5=a4+7=16
Then the sequence is 0, 1, 4, 9, 16
That is, an = (n-1) 2
a1=0;
a2=a1+2*1-1;
……
an=an-1+2*(n-1)-1;
Add both sides of equal sign
an+a1=0+2*1-1+2*2-1+…… +2*(n-1)-1;
an=(1+2n-3)*(n-1)/2
In known sequence an, A1 = 0, a (n + 1) = an + 2N-1. The general formula of an. The following is a general solution: let a (n + 1) + X * (n + 1) + y = an + X * n + y. put it into the test to solve the value of XY. Let BN = an + X * n + y solve the general term formula of BN. Reverse the general term of an
a1=0,a(n+1)=an+2n-1
So an = a (n-1) + 2 (n-1) - 1
a(n-1)=a(n-2)+2(n-2)-1
……
a2=a1+1
Add left and right to get it
The solution of equation 2 (X-2) - 3 (4x-1) = 9 (1-x) is?
2(x-2)-3(4x-1)=9(1-x)
Get rid of the brackets,
2x-4-12x+3=9-9x
It's very simple,
-10x-1=9-9x
Transfer of items,
-x=10
So, x = - 10
This is my answer
2x-4-12x+3=9-9x
-10x+9x-1=0
-x-1=0
x=-1
x=-10
Let x1.x2 be the two roots of the equation 2x-5x-1 = 0, and find 1 / X1 + 1 / x2
Let ax & # 178; + BX + C = 0 be X1 and x2,
Then: X1 + x2 = - B / A
x1*x2=c/a
It is known that X1 and X2 are the two roots of the equation: 2x & # 178; - 5x-1 = 0,
Then: X1 + x2 = 5 / 2
x1*x2=-1/2
So: 1 / X1 + 1 / x2 = (x1 + x2) / (x1 * x2) = (5 / 2) / (- 1 / 2) = - 5
Weida's theorem: let ax & # 178; + BX + C = 0 be X1 and x2,
Then: X1 + x2 = - B / A
x1*x2=c/a
It is known that X1 and X2 are the two roots of the equation: 2x & # 178; - 5x-1 = 0,
Then: X1 + x2 = 5 / 2
x1*x2=-1/2
So: 1 / X1 + 1 / x2 = (x1 + x2) / (x1 * x2) = (5 / 2) / (- 1 / 2) = - 5
1 / (3 + radical 33)
Let x1.x2 be the two roots of the equation 2x-5x-1 = 0, and find 1 / 1 of X1 + 1 / 2 of x2
x=[-b±√(b^2-4ac)]/2a=[5±√(5^2+4×2)]/4=[5±√33/4] x1=[5+√33]/4 x2=[5-√33]/4
Then: 1 / X1 + 1 / x2 = - 5
1/x1+1/x2=(x1+x2)/x1x2=(5/2)/(-1/2)=-5
Some problems about the general term formula of sequence of numbers
1. The sequence can be represented by {an}. Can an be represented by any number in the sequence or by a general formula?
2. Is an a value or a formula?
3. The definition of general term formula is the relationship between the number of terms n and the nth term an. What does an here mean? Is it a number
4. Is an and an of item n different concepts?
I think the meaning of an is much simpler than the description of the landlord. Now there is a sequence. In order to describe it, I stipulate that the first number is A1, and the second number is A2. In special cases, I can get its value according to its serial number, and the relationship is an =. The landlord can understand the above. This definition is very basic. It doesn't need to be studied deeply, and I can use it
The solution of the equation x ^ 2-4x = 3 I can't do
x^2-4x=3
x^2-4x+4=3+4=7
(x-2)^2=7
x-2=±√7
x=2±√7
^What's this?
If the value of the fraction 5x-5 / xsquare-1 is an integer, then x=
It is known from the meaning of the question that (5x - 5) / (X2 - 1) = 5 / (x + 1) is an integer, x + 1 = - 5 or - 1 or 1 or 5, x = - 6 or - 2 or 0 or 4
(5x-5)/(x^2-1)=5/(x+1)，∈Z，
——》X + 1 = + - 5 or + - 1, X-1 ≠ 0,
——》x=-6、-2、0、4。