If point C is a point on line AB and the square of AC equals AB times BC, is point C the golden section point of line AB

If point C is a point on line AB and the square of AC equals AB times BC, is point C the golden section point of line AB

Point C is the golden section of line ab
Let AB = 1, AC = X
Then x ^ 2 = 1 * (1-x)
x^2+x-1=0
X = (radical 5-1) / 2 = 0.618
So point C is the golden section of line ab
What are the three roots of equation x3-1 = 0? How to find out if there are two imaginary roots?
X 3 - 1 = (x - 1) (x ^ 2 + X + 1), and then the root formula of quadratic equation with one variable is used
(x^2+x+1)=0
Let's look at the discriminant. It's less than zero
So there is no solution in the real range
Or the solution set is empty
There is a real solution x = 1
There are two imaginary number solutions x = - 1 / 2 + (√ 3 / 2) I, the imaginary number: 1 + X + x ^ 2 = 0, x ^ 3 = 1, the conjugate of X multiplied by x = 1
x=-1/2-（√3/2）i
Let X be a complex number, x = a + bi, x ^ 3 = 1, imaginary part is 0, real part is 1
It's 1, the imaginary part is 0
According to a = a + bi
Substituting A3 = 1 of the above formula, we get
And because the real part is 1 and the imaginary part is zero, you can get the answer
X ^ 3-1 = (x-1) (x ^ 2 + X + 1) = 0 a root is x = 1
x^2+x+1=0
x^2+x+1/4+3/4=0
(x+1/2)^2+3/4=0
(x+1/2)^2=-3/4=（√3/2i)^2
x+1/2=±√3/2i
x=-1/2±√3/2i
So the other two are - 1 / 2 + √ 3 / 2I and - 1 / 2 - √ 3 / 2I respectively
Given that point C is the golden section of line AB, and AC > BC, AB equals 2, then BC equals?
BC=2x(1-0.618)=0.764
How to solve this equation
1.8X-8=X+8
1.8x-x=8+8
0.8x=16
x=16÷0.8
x=20
Hello:
1.8X-8=X+8
1.8x-x=8+8
0.8x=16
x=16÷0.8
x=20
1.8x＋x＝8+8
2.8x＝16
X = self calculation
1.8X-8=X+8
Solution: 1.8x-x = 8 + 8
1.8X-X=16
0.8X=16
X=20
1. If the condition AC squared = AB multiplied by BC, is point C still the golden section point of line AB? Why?
2. Does line AB have a golden section point other than point C? Why?
3. If AB = 1, then AC = -, BC = -, why?
If AB = a, then AC = --, BC = --, why?
Just answer questions 1 and 2
1. If the condition AC squared = AB multiplied by BC, then point C is still the golden section point of line AB? Why? Or? Because: AC & # 178; = AB * BCAC / AB = BC / ac2. Does line AB have any golden section point other than point C? Why? There are two golden section points on line ab
How to solve the equation x & # 178; - 8x = 0 by factorization
x²-8x=0
x（x-8）=0
X = 0 or X-8 = 0
Namely:
X = 0 or x = 8
Point P is the golden section point on line ab. if the longer line Pb = 4, the shorter line PA =, ab =
Specific steps, thank you
∵ point P is the golden section point on line ab
∴PA:PB=PB:AB
∵AB=PA+PB
∴PA:PB=PB:(PA+PB)
Then PA: 4 = 4: (PA + 4)
PA²+4PA=16
PA²+4PA-16=0
You can't wait for the exact number
Because the golden ratio is an infinite non cyclic decimal, the approximate value is 0.618
So PA = 4 × 0.618 = 2.472
AB = PA+PB = 6.472
X (X-2) = x (use factorization to solve this equation,
Point P is the golden section point of line AB, and PA > Pb (1) the relationship between line PA, Pb and ab is? (2) if AB = 8, Pb ≈?
(3) If the area of a square with PA as the side is S1, and the area of a rectangle with Pb and ab as the adjacent sides is S2, guess the size relationship between S1 and S2? Explain the reason
1) ∵ point P is the golden section point of line ab
∴PB:PA=PA:AB=(√5-1)/2;PA²=PB*AB
2)∵PA=(√5-1)/2*AB=4(√5-1)
∴PB=(√5-1)/2*PA
=2(√5-1)²
=2(6-2√5)
=12-4√5
∵S1=PA²,S2=PB*AB;PA²=PB*AB
∴S1=S2
The factor decomposition method is used to calculate
(1) -7ab-14abx+49aby; (2) (x-1)^3y^3+(1-x)^3z^3;
(3)(x^2+x)^2 -3(x^2+x)+2; (4) x^2-y^2-z^2+2yz;
(5)3x^2+2xy-8y^2; (6) x^2-x-30; (7) x^4+4.
(1) -7ab-14abx+49aby; = -7ab（1+2x-7y） (2) (x-1)^3y^3+(1-x)^3z^3=（x-1）³（y³-z³）=（x-1）³（y-z）（y²+yz+z²）(3)(x^2+x)^2 -3(x^2+x)+2; =（x²+x-1）（x²+x-2）=...