Use formula method to solve equation: Y (y-4) = 2-8y, use factorization method to solve equation: (3x-1) square = (x + 1) square Solve the above two equations process, urgent!

Use formula method to solve equation: Y (y-4) = 2-8y, use factorization method to solve equation: (3x-1) square = (x + 1) square Solve the above two equations process, urgent!

y(y-4)=2-8y
y^2-4y+8y-2=0
y^2+4y-2=0
d=4^2+4*2=24
y=(-4±√d)/2=(-4±2√6)/2=-2±√6
(3x-1)^2=(x+1)^2
(3x-1)^2-(x+1)^2=0
(3x-1+x+1)(3x-1-x-1)=0
4x*(2x-2)=0
8x(x-1)=0
x=0,1
y(y-4)=2-8y
y²-4y+8y=2
y²+4y+4=6
(y+2)²=6
y=-2+√6 y=-2-√6
The square of (3x-1) = the square of (x + 1)
3x-1=x+1 3x-1=-x-1
2x=2 4x=0
x=1 x=0
How to solve the formula of the square of y-12y-12 = 0
y1=(12+sqrt(12*12+4*12))/2=6+4*sqrt(3)
y2=(12-sqrt(12*12+4*12))/2=6-4*sqrt(3)
Sqrt () is the root sign, * is the multiplication sign, / is the division sign
In general, for a bivariate quadratic equation AX ^ + BX + C = 0 (a is not equal to 0), when B ^ - 4ac > = its roots are ([- B + √ (b ^ - 4ac)] / 2a, [- B - √ (b ^ - 4ac)] / 2A)
The same solution of equation 4x = 8y and x = 2Y
4x=8y
Divide both sides by 4
The solution of the equation is invariant
We get x = 2Y
Therefore, the equation 4x = 8y and x = 2Y have the same solution
Why?
Limx (√ (X & # 178; + 1) - x) x tends to infinity, find the limit
Multiplication √ (X & # 178; + 1) + X
Then the molecule is the difference of squares
The molecule is x [√ (X & # 178; + 1) - x] [√ (X & # 178; + 1) + x]
=x(x²+1-x²)
=x
So the original formula = limx / [√ (X & # 178; + 1) + x]
Divide up and down by X
=lim1/[√(1+1/x²)+1]
=1/2
How to deduce the summation formula of equal ratio sequence~
Equal ratio sequence A1 = a A2 = AQ A3 = AQ ^ 2 A4 = AQ ^ 3 an = AQ ^ (n-1) equal ratio sequence and S = a1 + A2 + a3 + A4 + ---- + an = a + AQ + AQ ^ 2 + AQ ^ 3 + ---- + AQ ^ (n-1) multiply both sides of the equation by Q: QS = AQ + AQ ^ 2 + AQ ^ 3 + ---- + AQ ^ (n-1) + AQ ^ n subtract the above two expressions to get (1-Q
The limit of (X & # 178; - 1) / (2x & # 178; - x-1) when x tends to ∞
We use a formula similar to SiNx / x = 1 instead of derivative
(X & # 178; - 1) / (2x & # 178; - x-1) the numerator denominator is divided by X & # 178; at the same time
lim（1-1/x²)/(2-1/x-1/x²)
=(1-0)/(2-0-0)
=1/2
How to use junior high school knowledge to deduce the summation formula of equal ratio sequence
Let the common ratio of the equal ratio sequence be K, and the i-th term be a {I}; the sum of the first n terms of s {n} table, then s {n} = a {1} + k * a {1} + (k ^ 2) * a {1} + +[k^(k-1)]*a{1}kS{N}= k*a{1}+(k^2)*a{1}+…… +[K ^ (k-1)] * a {1} + (k ^ k) * a {1} minus the above, we get (k-1) s {n} = a {1} * (k ^ k-1) when k is not equal to
How to find the limit of limx (√ (X & # 178; + 1) - x) when x →∞
What are the similarities and differences between linear equation with one variable, linear equation with two variables and quadratic equation with one variable?
The general form is ax + B = 0, (a ≠ 0); the general form is ax & sup2; + BX + C = 0 (a, B, C are constants, a ≠ 0)
Quadratic equation of one variable: an unknown number with the highest power of 2
Binary linear equation: two unknowns, the highest power is 1
"Yuan" stands for the number of unknowns
"Power" stands for power
The definition, the general form, I said. It is the biggest difference between the solution of its equation and the number of its solutions! Learning these is also a progressive relationship, first easy then difficult They are different!
Limx →∞ (√ x + 1 - √ x) for limit
limx→∞（√x+1-√x)
=limx→∞1/（√x+1+√x)
=0