(x + 1) (x-3) = 2x + 5 to solve the equation

(x + 1) (x-3) = 2x + 5 to solve the equation

(x+1)(x-3)=2x+5
x²-2x-3=2x+5
x²-4x=8
x²-4x+4=8+4
(x-2)²=12
x-2=±2√3
x=2-2√3,x=2+2√3
Teacher to a mathematical problem, urgent process!
As shown in the figure, in the plane rectangular coordinate system, for the circle with radius 1, the center O is at the origin of the coordinate and intersects with the two coordinate axes at points a, B, C, D and 4 respectively, the parabola y = ax & sup2; + BX + C intersects with the Y axis at D, intersects with the straight line y = x at points m and N, and Ma and NC are tangent to the circle O at points a and C respectively
(1) Solving parabola analytically?
(2) The symmetry axis of the parabola intersects the X axis at e, connects de and extends the intersection circle O of De to F, and calculates the length of EF?
(3) Make the tangent line of circle O through B and intersect DC with P to judge whether P is on the parabola?
Analytical formula: X & sup2; + Y & sup2; = 1
Let a (1,0), B (- 1,0), then AB is on a parabola,
The result is: a + B + C = 0
a-b+c=0
A = - C, and then using the tangent to get another relationship, we can get the parabola
Let BN = log2 | an |, tn be the sum of the first n terms of the sequence {1 / (n ^ 2 (bn-1))}
Verification of TN
(1) The general formula for solving {TN} is not written. The solution is TN = 1 / N ^ 3 (2). Since the landlord does not like to use mathematical induction to prove it, I will use the "expansion and contraction method" to prove it: 1 + 1 / 2 ^ 3 + 1 / 3 ^ 3 + 1 / 4 ^ 3 +1/n^3≤1+1/8 + 1/27 +1/(4*3*4)…… +1/[4*(n-1)*n]=1+1/8 + 1/2...
What number is a multiple of 3, a multiple of 5 or a factor of 7
105, 210, 315, etc
Why does Wahaha's mineral water cost 1.5 yuan per bottle?
Why don't you bid 2 Yuan directly? Do you have to find a trouble of 50 cents for 1.5?
Let {an} be the arithmetic sequence and {BN} be the proportional sequence, and A1 = B1 = 1, A3 + A5 = B4, b2b3 = A8, the sum of the first 10 terms of {an} and {BN} can be obtained respectively
Let the tolerance be D and the common ratio be Q
2+6d=q^3,
q^3=1+7d,
The solution is d = 1, q = 2
The sum of the first 10 terms of {an} = 10 + 10 * 9 / 2 = 55
The sum of the first ten terms of {BN} = 2 ^ 10-1 = 1023
According to the general idea, the tolerance is d
2+6d=q^3,
q^3=1+7d,
The solution is d = 1, q = 2
So: the sum of the first 10 terms of {an} = 10 + 10 * 9 / 2 = 55
The sum of the first ten terms of {BN} = 2 ^ 10-1 = 1023
What is the number that comes from adding 7 to a two digit number, which is a multiple of 2 and a factor of 3 and 5
It should be 23. 23 + 7 = 30. 30 is a multiple of 2. 30 is a multiple of 3. 30 is a multiple of 5
Hehe, it should be 53 or 83
Xiao Ming went to the store to buy drinks. The money he brought was more than three yuan for three bottles, but five yuan for five bottles. How much is each bottle?
Arithmetic method: (5 + 1) / (5-3) = 3 (yuan) [5 + 1 is price difference, 5-3 is bottle number difference]
If x yuan for each bottle of beverage is set, then:
3x+1=5x-5
The solution is: x = 3
That is 3 yuan per bottle
Let (ANSN = 4.8) be the general formula of arithmetic
It is known that (an) is an arithmetic sequence, and A4 = 14. A5 + A8 = 48,
1. General term formula for (an)
2 let Sn be the sum of the first n terms of the equal ratio sequence BN, if B1 = A1, and 3s1.2s2.s3 is an equal difference sequence, find S4
Let {an} tolerance be D and {BN} common ratio be q (Q ≠ 0)
a5+a8=a4+d+a4+4d=2a4+5d=2×14+5d=5d+28=48
5d=20 d=4
a1=a4-3d=14-3×4=14-12=2
an=a1+(n-1)d=2+4(n-1)=4n-2
The general formula of sequence {an} is an = 4n-2
b1=a1=2
If 3s1, 2s2 and S3 are equal difference sequence, then
2×(2S2)=3S1+S3
3S1+S3-4S2=0
3a1+a1+a2+a3-4(a1+a2)=0
a3=3a2
q=a3/a2=3
S4=b1(q^4 -1)/(q-1)=2×(3^4 -1)/(3-1)=80
A number is a multiple of three, a multiple of five, and a factor of seven______ .
3. 5 and 7 are coprime, so the least common multiple of 3, 5 and 7 is 3 × 5 × 7 = 105