Point C is the golden section of line AB, (AC > BC), then BC=______ AC．

Point C is the golden section of line AB, (AC > BC), then BC=______ AC．

∵ point C is the golden section of line AB, (AC > BC), ∵ AC = 5 − 12ab, ∵ AB = 5 + 12ac, ∵ BC = AB-AC = 5 + 12ac-ac = 5 − 12ac
What is the substitution method of factorization? Can you give me some questions? I'm not good at it!
Thank you!
Come on! Twelve methods of factorization transform a polynomial into the product of several integers. This kind of transformation is called factorization of the polynomial. There are many ways of factorization, which are summarized as follows: 1
Dissolve (X & sup2;) & sup2; + 2x & sup2; + 1 =?
On the mathematical problems of golden section
1. The length of line segment AC is m, AB > BC, and there is golden section in the line segment?
It should be AB / BC = BC / AC, let BC = x, then AB = M-X
So (M-X) / x = x / M
The result is: x ^ 2 + mx-m ^ 2 = 0
Rounding off the negative solution according to the root formula
The solution is x = 0.618m
The exact golden section ratio is: (√ 5-1): 2, that is, the longer segment: the total length = (√ 5-1): 2 ≈ 0.618:1
According to your question, there is ab: AC = 0.618:1, so AB = 0.618ac = 0.618m
I know that too.. I'll tell you the total length is m?
A mathematical factorization, using the substitution method
(6x-1)(2x-1)(3x-1)(x-1)+x^2
(6x-1) (2x-1) (3x-1) (x-1) + x ^ 2 = [(6x-1) (x-1)] [(2x-1) (3x-1)] + x ^ 2 = (6x ^ 2-7x + 1) (6x ^ 2-5x + 1) + x ^ 2 let a = 6x ^ 2 + 1 primitive = (a-7x) (a-5x) + x ^ 2 = a ^ 2-12ax + 36x ^ 2 = (a-6x) ^ 2 = (6x ^ 2-6x + 1) ^ 2
Solving mathematical problems related to golden section,
1. It is known that P and Q are the two golden section points of line AB, and ab = 10cm, then the length of PQ is () a, 5 (radical 5-1) B, 5 (radical 5 + 1) C, (10 radical 5-2) d, 5 (3-radical 5) 2
Solving a factorization with the method of substitution
(x square + 5x + 6) (x square + 7x + 6) - 3 x square
Let x ^ 2 + 6 be a and have (a + 5x) (a + 7x) - 3x ^ 2
The result is a ^ 2 + 15ax + 33x ^ 2
Cross phase multiplication (a + 3x) (a + 11x)
Recover to (x ^ 2 + 3x + 6) (x ^ 2 + 11x + 6)
The golden section
Dear uncles, aunts, brothers and sisters, I put forward that the golden section ratio is about 1:1.615,
1/x=(x-1)/1
x^2+-x-1=0
X = (1 ± √ 5) / 2, (negative root omitted)
x≈1.618
The golden ratio is about 1:1.618
It's not right. Didn't your teacher teach you? 0.618 is the golden section... X²
√5-1/2
The standard is 0.618, you may have a deviation in the calculation, ha ha, it's not urgent, just do it again
According to your number into a decimal is 0.8695652174, so determine your miscalculation, give me the question, I will calculate for you
golden section
A line segment is divided into two parts so that the ratio of one part to the whole length is equal to the ratio of the other part to this part. The ratio is an irrational number, and the approximate value of the first three digits is 0.618. Because the shape designed according to this proportion is very beautiful, it is called golden section, also known as Sino foreign ratio. This is a very interesting number. We take 0.618 as an approximation. Through simple calculation, we can find that:
1/0.618=1.618
(1-0.618)/0.618=0.618
The expansion of this number
golden section
A line segment is divided into two parts so that the ratio of one part to the whole length is equal to the ratio of the other part to this part. The ratio is an irrational number, and the approximate value of the first three digits is 0.618. Because the shape designed according to this proportion is very beautiful, it is called golden section, also known as Sino foreign ratio. This is a very interesting number. We take 0.618 as an approximation. Through simple calculation, we can find that:
1/0.618=1.618
(1-0.618)/0.618=0.618
The function of this value is not only reflected in the art fields such as painting, sculpture, music and architecture, but also plays an important role in management and engineering design. Put it away
Mathematical golden section problem
(1) Scientific research shows that when a person's lower limbs to height ratio is 0.618, she looks the most beautiful. An adult woman's height is 153cm, and her lower limbs are 92cm. What is the optimal height of the heel of the high-heeled shoes she wears? (accurate to 0.1cm) (attached)
(2) If line AB = 4cm and point C is a golden section point of line AB, what is the length of AC?
(3) When the temperature is at the golden ratio of normal body temperature (36 ℃ ~ 37 ℃), people feel most comfortable. Therefore, when using air conditioning in summer, it is most appropriate to adjust the indoor temperature to ▁▁,
1. Set the height of high heels xcm, 0.618 (153 + x) = 92 + X, X ≈ 6.7
2. Let AC = x, then 4-x / x = x / 4, x = 2 times the root 5-2
3. About 23
Mathematical golden section problem
If line AB = 10cm, point P is the point on line AB and AP: BP = BP: AB is satisfied, then the ratio of AP: BP is___
Let AP = x, then BP = 10-x
If AP: BP = BP: AB, then AP * AB = BP & #
That is: 10x = (10-x) &# 178;, X & # 178; - 30x + 100 = 0
b²-4ac=900-4*1*100=500.
∴x=(30±√500)/2=(30±10√5)/2=15±5√5.
Then AP = 15-5 √ 5
∴BP=10-X=5√5-5.
AP:BP=(15-5√5)/(5√5-5)=(√5-1)/2.
As shown in the figure, point C is the golden section point of line AB, AC = 2, then ab · BC=______ .
The answer to this question is: 4