To solve the linear equation of three variables {14x-4y + 2Z = 9.3x + 2Y + 4Z = - 2,6x-4y-2z = 7

To solve the linear equation of three variables {14x-4y + 2Z = 9.3x + 2Y + 4Z = - 2,6x-4y-2z = 7

(1) + (3) get
20x-8y=16
5x-2y=4 (4)
(2) + (3) × 2
15x-6y=12
5x-2y=4 (5)
(4) (5) is the same equation
The equation has more than one set of solutions
The solution equation: (3y-1) / 2 = y (3-y) / 3; (3x-0.4) / 0.4 + 0.5 = (15-14x) / 2
It is (3y-1) / 2 = y - (3-y) / 3
（3y-1）/2=y-（3-y)/3
y=-3/5
（3x-0.4）/0.4+0.5=（15-14X)/2
x=280.4/283
Sorry, we didn't learn it
Sorry, I didn't learn it
y=(-3±(33)^0.5)/4
x=16/29
The mathematical equation 3x-14x + 16 = 0 solves the equation
Factorization of original equation
We get (3x-8) (X-2) = 0
The solution is x = 8 / 3 or x = 2
3x²-14x+16=0
﹙x－2﹚﹙3x－8﹚＝0
x1=2, x2=8／3
(3x-8)(x-2)=0
x=8/3 x=2
3x²-14x+16=0
(x-2)(3x-8)=0
x1=2
x2=8/3
Multiply 3x ^ 2-14x + 16 = 0 by cross
3 -8
1 -2
We get X1 = 8 / 3, X2 = 2
At the same time, it can be obtained by formula method
The general term formula of sequence without observation
How to find the general term formula without using the observation method?
____ Write a sequence function randomly, the result may not be complex, but the original sequence function can be infinitely complex, so it is almost infinitely difficult to inverse the sequence function according to the sequence result! If there is such a complex logic, it will be too complex to use! The formula solution of the cubic and quartic equation with one variable is the same, It's too complex to be useful! People realize this and don't invest in research unnecessarily!
____ In fact, observation is a unique way of thinking of human beings. It contains a large number of random and effective choices, which can not be included in any mathematical formula. Even artificial intelligence can only be imitated in theory. Therefore, we should not underestimate observation, which is the most intelligent embodiment of earth creatures, Only human beings can play it to the extreme!
____ If you look around, you will soon get a general idea of what's going on around you. Which machine or mathematical method can do this?
As long as the first few values are met, they are all general term formulas. So there are countless...
Proof method (prove to be equal difference or equal ratio), transformation method: Transform to equal difference and equal ratio after deformation, such as an + P = q (an-1 + P), know that the first N-term sum can be done by sn-sn-1 = an, n > = 2
I can't ask.
What's the solution to equation 45-4x = 13
45-4x=13
-4X=13-45
-4X=-32
X=8
45-4x=13
4x=45-13
4x=32
X=8
45-4x=13
==>4x=45-13
==>4x=32
==>x=8
45-4x=13
45-13=4x
4x=32
X=8
X=8
45-4x=13
45-13=4x
4x=32
X=8
The solution of general term formula of sequence
The elements in the sequence are 1 3 6 10 15 21 How to find the general term formula of
It can be seen as 1 1 + 2 1 + 2 + 3 So the formula of arithmetic sequence is n (n + 1) / 2
On the equation of X, the solution of AX + 2 = 4x is a natural number, then the value of integer a is
ax+2=4x
4x-ax=2
(4-a)x=2
When 4-A = 0, the equation does not hold
X = 2 / (4-A) is a natural number, that is, x = 1 or x = 2
4-A = 2 or 4-A = 1
A = 2 or a = 3
a=2,x=1
When to use superposition to find the general term formula?
When we meet the recurrence relation of a (n + 1) - A (n) = f (n), we consider the superposition method to find the general term formula
If a (n + 1) - A (n) = 2n and A1 = 1,
Then a2-a1 = 2 × 1
a3-a2=2×2
a4-a3=2×3
……………
a(n)-a(n-1)=2(n-1)
Add the left and right sides of the above equations to get a (n)
Finding the value of unknown X by equation x-3 / 4x = 3 / 8
Multiply both sides by 8,
It turns into 8x-6x = 3,
That is, 2x = 3,
So Χ = 3 / 2, or x = 1.5
complete.
3/2
x-3/4x=3/8
1/4x=3/8
x=3/2
1/4x=3/8
x=3/2
3 / 2 question: calculation process
How to find {f (n)} on the right side of the general term formula by superposition method?
How to stack the f (n) on the right? For example, in this problem, in the sequence {an}, A1 = 2, a [n-1] - an = 3N, then the general term an of the sequence {an} and other methods such as superposition and multiplication, addition in reverse order, dislocation subtraction, etc
a[n]=3n+a[n-1],a[n-1]=3(n-1)+a[n-2]… A [2] = a [1] + 6, add up to a [n] = 2 + (6 + 9 +) +3n) = 2 + 3 / 2 times (2 + n) (n-1)