C is the golden section point of line AB, AC > BC, then the square of AC

C is the golden section point of line AB, AC > BC, then the square of AC

=BC*AB
=AB*BC
Polynomial y = a2-4ab + 5b2-2b + 2001, when a, B respectively take what value, y get the minimum value?
If for any value x, there is always X & # 178; + 3x + 2 = (x-1) &# 178; + m (x-1) + N, find the values of M and n
It is the last question of 40 pages in the series of seven learning methods of mathematics
It's urgent. Thank you
X & # 178; + 3x + 2 = (x-1) &# 178; + m (x-1) + NX & # 178; + 3x + 2 = x & # 178; - 2x + 1 + mx-m + NX & # 178; + 3x + 2 = x & # 178; + (m-2) x + (1-m + n) the corresponding coefficients are equal, get: m-2 = 31-m + n = 2 solution: M = 5, n = 6 do not know how to ask ~ I hope my answer is helpful to you, take o (∩)_ ∩)O!...
As shown in the figure, given that point C and point D are the golden section points of line AB, CD = 6, let AB be set
Do it by setting the number of copies, and set AC as X
BC = AB-AC = AB-(AD-CD) = AB-AD+CD
1-AD/AB + CD/AB = AD/AB
1 + CD / AB = 2ad / AB = radical (5) - 1
CD / AB = radical (5) - 2
AB = CD / (radical (5) - 2) = CD (radical (5) + 2) = 6 radical (5) + 12
A2 + 2B2 = 6, what is the minimum value of a + B
Solution 1: discriminant method
Let a + B = t, then a = t-b. [1]
The substitution condition is: (T-B) ^ 2 + 2B ^ 2 = 6,
3b^2-2tb+(t^2-6)=0.[2]
∵ B is a real number, Δ ≥ 0,
That is, 4T ^ 2-12 (T ^ 2-6) ≥ 0,
It is reduced to T ^ 2 ≤ 9,
∴-3≤t≤3.
When t = - 3, B = - 1 is obtained from [2], and a = - 2 is obtained by substituting [1]
So the minimum value of a + B is - 3 (when a = - 2, B = - 1)
Solution 2: trigonometric substitution
a^2+2b^2=6→(a^2)/6+(b^2)/3＝1,
Let a = (root 6) cosx, B = (root 3) SiNx, where x ∈ R
A + B = (root 3) SiNx + (root 6) cosx
=Under the root sign [(root 3) ^ 2 + (root 6) ^ 2] sin (x + θ). [1]
=3sin (x + θ), (where θ is the auxiliary angle)
The minimum value of sin (x + θ) is - 1,
So the minimum value of a + B is - 3
Note: formula [1] uses the formula: asinx + bcosx = root (a ^ 2 + B ^ 2) * sin (x + θ),
The "auxiliary angle θ" satisfies the condition "Tan θ = B / a", and the quadrant position of auxiliary angle θ is determined by the quadrant position of point (a, b)
The known set a = {x │ X & # 178; - x-120}, C = {x │ x ^ 2-4ax + 3A ^ 2}
Yes (a ∩ b)
A={x|-3
A:X^2-X-12
As shown in the figure, ab = 2, point C is the golden section of line AB, point D is on AB, and the square of ad = BD
Ad ^ 2 = BD * AB indicates that point D is also the golden section point of line ab
From the golden section ratio (√ 5-1) / 2, we get ad = √ 5-1
If C and d do not coincide, then BC = √ 5-1, AC = 3 - √ 5
CD=AD-AC=2√5-4
CD/AC=(2√5-4)/(3-√5)
=(√5-1)/2
When the values of a and B are what, the polynomial A2 + 2Ab + 2B2 + 6B + 18 has the minimum value? And find the minimum
∵ A2 + 2Ab + 2B2 + 6B + 18 = A2 + 2Ab + B2 + B2 + 6B + 9 + 9 = (a + b) 2 + (B + 3) 2 + 9, ∵ the minimum value of polynomial A2 + 2Ab + 2B2 + 6B + 18, ∵ B + 3 = 0, B = - 3; a + B = 0, a = 3; the minimum value of polynomial is 9
Let m = {x | X & # 178; - 4ax + 3A & # 178; > 0, a > 0}
Let m = {x | X & # 178; - 4ax + 3A & # 178; > 0, a > 0}, n = {x | extra large bracket X & # 178; - 5x-14 ≤ 0}, if M ∪ n = R, find the value range of A
Extra large bracket X & # 178; + 2x-8 > 0
Extra large brackets and extra large brackets are the meaning of equations
∵x²-4ax+3a²>0 ,a>0
∴M={x|x3a,a>0}
∵x²-5x-14≤0 x²+2x-8>0
■ - 2 ≤ x ≤ 7 and X2
∴N={x|2
If point C is the golden section of line AB and AC > BC, then ABAC = 0___ ，BCAB= ___ .
Acab = BCAC = 5-12, ABAC = 25-1 = 5 + 12, bcab = 3-52