Factorize (a ^ 2 + B ^ 2-2) (a ^ 2 + B ^ 2) - 24 = 0 and a + B = 3 by substitution method

Factorize (a ^ 2 + B ^ 2-2) (a ^ 2 + B ^ 2) - 24 = 0 and a + B = 3 by substitution method

Let a ^ 2 + B ^ 2 = m (a ^ 2 + B ^ 2-2) (a ^ 2 + B ^ 2) - 24 = m ^ 2-2m-24 = (M-6) (M + 4) = 0  M = 6 or M = - 4, that is, a ^ 2 + B ^ 2 = 6, a ^ 2 + B ^ 2 = - 4 (rounding off) a + B = 3 - > A ^ 2 + 2Ab + B ^ 2 = 9, ab = 3 / 2 and a + B = 3. The simultaneous solution of a = 3 / 2 + √ 3 / 2, B = 3 / 2 - √ 3 / 2 or a = 3 / 2 - √ 3 / 2, B = 3 / 2 + √ 3 / 2
Formula method, factorization,
1.1002^2-1002×4+4
2.80062-1600×798+798^2
1.1002^2-1002×4+4
=1002^2-2×2×1002+2^2
=(1002-2)^2
=1000^2
=1000000
2.800^2-1600×798+798^2
=800^2-2×800×798+798^2
=(800-798)^2
=2^2
=4
Formula method, factorization,
Don't simplify the process
1.（x-2y)^2+ 14(2y-x)+49
2.(x+2y)^3- (x+2y)
1.（x-2y)^2+ 14(2y-x)+49
=（x-2y)^2-2*7*(x-2y)+49
=(x-2y-7)^2
2.(x+2y)^3- (x+2y)
=(x+2y)[(x+2y)^2-1]
=(x+2y)(x+2y+1)(x+2y-1)
.（x-2y)^2+ 14(2y-x)+49
=(x-2y-7)^2
2.(x+2y)^3- (x+2y)
=(x+2y)[(x+2y)^2-1]
=(x+2y)(x+2y+1)(x+2y-1)
1.（x-2y)^2+ 14(2y-x)+49
=[（x-2y)+7]^2
=(x-2y+7)^2
2.(x+2y)^3- (x+2y)
=(x+2y)[(x+2y)^2-1]
=(x+2y)(x+2y+1)(x+2y-1)
1. Formula A ^ 2-2ab + B2 = (a-b) ^ 2
（x-2y)^2+ 14(2y-x)+49=（x-2y)^2- 14(x-2y)+49=（x-2y)^2- 2*7(x-2y)+7^2=(x-2y-7)^2
2. Formula A ^ 3-A = a (a ^ 2-1) = a (a + 1) (A-1)
(x+2y)^3- (x+2y)=(x+2y)((x+2y)^2-1)
=(x+2y)(x+2y+1)(x+2y-1)
1. Formula A ^ 2-2ab + B ^ 2 = (a-b) ^ 2
（x-2y)^2+ 14(2y-x)+49=（x-2y)^2- 14(x-2y)+49=（x-2y)^2- 2*7(x-2y)+7^2=(x-2y-7)^2
2. Extract the common factor a first,
Then a (a ^ 2-1) = a (a + 1) (A-1)
(x+2y)^3- (x+2y)=(x+2y)((x+2y)^2-1)
=(x+2y)(x+2y+1)(x+2y-1)
Point C is the golden section point of line AB, ab = 2, then the value of AC is?
Because point C is the golden section of ab
Therefore, AC / AB = BC / AC = 0.618
AC = 1.236 or 0.764 (because point C doesn't tell you exactly which segment is long)
one point two three six
zero point seven six four
If point C makes line AB golden section, and AC > BC, AC = 2cm, then BC=______ .
∵ point C is the golden section point (AC ＞ BC) of line AB, ∵ AC = 5 − 12ab, AC = 2cm, ∵ AB = (5 + 1) cm, ∵ BC = AB-AC = 5 + 1-2 = (5-1) cm
Given that line AB = 2cm, point C is the golden section point of line AB, calculate AC
AC / AB = 0.618 or BC / AB = 0.618 ab-bc = AC
So there are two results
If point C is the golden section of line AB, and the longer line AC = 2cm, then the length of AB is?
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 [5 ^ (1 / 2) - 1] / 2, and the approximate value of the first three digits is 0.618. So AB = AC / ([√ 5-1] / 2) = (1 + √ 5) cm
Point C is the golden section point (AC > BC) of line ab. if AB = 2cm, then AC = () BC = () BC of AC = () process
Because the golden ratio is "1:0.618", and (AC > BC)
So let AC = x, BC = 0.618x,
According to ab = 2cm, ab = AC + BC, the following equation can be listed:
2cm=x+0.618x
The solution is about 1.236
So AC = 1.236cm
bc=0.764cm
BC = (1.236 / 0.764) is about 1.618 ∶ 1 = golden section ratio
(I don't know whether the landlord needs fractions or decimals, so I will use decimals to calculate according to our requirements, so in the process of solving the problem, there will be about equal to. If the landlord needs it, just change it to fractions ~)
Let AC = xcm, then BC = (2-x) cm
According to the definition of golden section, AC ^ 2 = BC · ab
∴x^2＝2(2－x)
∴x^2＋2x－4＝0
The solution is: x = √ 5-1 or x = - √ 5-1 (rounding off)
How can no one answer this question? I mentioned offering reward 115 and using props. Is that right? If you ask for the value of AC, BC and BC / AC, then it must be expanded
Let AC = xcm, then BC = (2-x) cm
According to the definition of golden section, AC ^ 2 = BC · ab
∴x^2＝2(2－x)
∴x^2＋2x－4＝0
The solution is: x = √ 5-1 or x = - √ 5-1 (rounding off)
Q: how come no one answered this question? I mentioned offering a reward 115 and used props. Is that right
Line AB = 1, C is the golden section point of AB, what is AC equal to
Do it as an answer
AC/AB =0.618/1
Then AC = radical 5-1
Solution: AC ≈ 0.618 defined by golden section
If point C is the golden section of line AB close to B, then AC is equal to 2, then AB is equal to?
∵ point C is the golden section of line AB near B
∴AC：AB=[（√5）-1]：2
And ∵ AC = 2
That is, 2: ab = [(√ 5) - 1]: 2
∴AB=4/[（√5）-1]
=（√5）+1
If decimal form is needed, ab ≈ 3.236