Given that point P is the golden section point on line AB, the longer line segment Pb is 4 cm, then the shorter line segment PA = cm, ab = cm

Given that point P is the golden section point on line AB, the longer line segment Pb is 4 cm, then the shorter line segment PA = cm, ab = cm

Because point P is the golden section point on line AB, and Pb is the longer line segment,
So Pb = [(radical 5 -- 1) / 2] ab
Because Pb = 4cm,
So AB = 8 / (radical 5 -- 1) = 2 (radical 5 + 1) cm,
PA = AB -- Pb = 2 (radical 5 -- 1) cm
Root 3x = root 2 [x + 1] [X-1]
The calculation method of factorization is the simplest one
Root 3x = root 2 [x + 1] [X-1]
3X=2(X^2-1)
2X^2-3X-2=0
(X-2)(2X+1)=0
X1 = 2, X2 = - 1 / 2
If P is the golden section of line AB (PA is greater than Pb), ab = 8cm, then AP = ()
I just looked at the question again
It's 8 × 0.618 = 4.944
According to the definition of golden section point, combined with the theme:
AP=（√5-1）/2 AB
=（√5-1）/2*8
=4（√5-1）
=4.944
Calculation by simple method (formula method of factorization)
(1 / 2 of 1-2) (1 / 2 of 1-3) (1 / 2 of 1-4). (1 / 2 of 1-100)
(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/100²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/100)(1+1/100)=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5).(100/99)(99/100)(101/100)=(1/2)(101/100)=1...
Let C be the golden section point of line AB, and let d be the point of line AC so that CD = CB. Let d be the golden section point of line ca
Let AB = a, then BC = (root 5-1) a / 2= CD.AC=AB -BC = (3-root 5) a / 2
CD: AC = (root 5-1) / (3-root 5) = (root 5-1) / 2, that is, D is the golden section point of line ca
Factorization with formula method
The fifth power of XY - the fifth power of 81x y
The fifth power of XY - the fifth power of 81x y
=xy(y⁴－3⁴x⁴)
=xy(y²＋9x²)(y²－9x²)
=xy(y²＋9x²)(y＋3x)(y－3x)
The fifth power of XY - the fifth power of 81x, y, is equal to:
First, we propose the common factor XY, then we have the fourth power of Y - the fourth power of 81x.
The fourth power of Y is the fourth power of 81x. We can use the square difference formula to treat the fourth power of Y as the square of the square of Y.
Next you will. Question: Well, thank you for your answer
If point C is the golden section of line AB, AC is a longer line and AC = 2, then AB is better than BC = ()
It's not AB than BC, it's AB times BC = ()
If point C is the golden section of line AB, AC is a longer line and AC = 2, then ab × BC = (4)
Point C is the golden section of line ab
ab：ac=ac：bc
ab×bc=ac ²=4
Please click the [select as satisfactory answer] button below,
2x²+7x-4
3x²+5x-2
5x²-2x-16
2x²+7x-4
=(2x-1)(x+4)
3x²+5x-2
=(3x-1)(x+2)
5x²-2x-16
=(5x+8)(x-2)
What is the golden section?
It's said on the Internet:
The golden section, also known as the golden rule, refers to a certain mathematical proportional relationship between the parts of things, that is, the whole is divided into two parts, the ratio of the larger part to the smaller part is equal to the ratio of the whole to the larger part, and the ratio is 1 ∶ 0.618 or 1.618 ∶ 1, that is, the ratio of 0.618.0.618 of the whole section is considered to be the most aesthetically significant, So it is called golden section
However, in my opinion, multiply a number by 0.618, and the result is the golden ratio
A line segment AB, if point C is the golden section of AB, then AC ratio AB equals BC ratio AC, that is, the square of AC equals AB times BC
A problem of factorization
3x^2-2x+1/3
3(x^2-2x/3+1/9)=3(x-1/3)^2
3x^2-2x+1/3
=1/3(9x²-6x+1)
=1/3(3x-1)²