A problem of solving quadratic equation of one variable in the third grade of junior high school 2m & sup2; - 1 = 5m, 1 / N & sup2; + 5 / N = 2 and m ≠ n, find 1 / M + 1 / n

A problem of solving quadratic equation of one variable in the third grade of junior high school 2m & sup2; - 1 = 5m, 1 / N & sup2; + 5 / N = 2 and m ≠ n, find 1 / M + 1 / n

2m²-1=5m2m²-5m-1=0………… ①1/n²＋5/n=22n²-5n-1=0………… ② It can be seen that we can regard m and N as the two roots of the equation: 2x & sup2; - 5x-1 = 0, which have the Weida's theorem: M + n = 5 / 2Mn = - 1 / 2 ∧ 1 / M + 1 / N = (M + n) / Mn = 5 / 2 ∧ - 1

Convert (x + 1) ² = (2x + 1) ² - 3 to the form of (x-m) ² = n, and find the value of M + 3N
Given the equation (M + 1) x & # 178; + 2mx-3 = m, it must be ()
A. Univariate quadratic equation
C. Univariate quadratic equation or univariate quadratic equation & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; D. cannot be determined
Because the ability of understanding is not flattering. So please explain it in detail~

First question
(x+1)^2=(2x+1)^2-3
x^2+2x+1=4x^2+4x+1-3
3x^2+2x-3=0
3(x^2+2/3x+1/9)-3-1/3=0
3(x+1/3)^2=10/3
(x+1/3)^2=10/9
The second question, when m = - 1, it is a linear equation with one variable, and when m ≠ - 1, it is a quadratic equation with one variable

In the third year of junior high school, the problem of quadratic equation of one variable is solved by formula method
(3-y) square = 2Y (Y-3)
3x square - (x + 2) square + 2x = 0
It's not convenient to type symbols on mobile phones. Let's make do with it
Can you be more specific about the process? I don't have a good brain
We must use the formula method

9-6y + y ^ 2 = 2Y ^ 2-6y, that is, y ^ 2-9 = 0, (Y-3) (y + 3) = 0. According to the square difference formula, the solution of the equation is y = 3 or y = - 3
3x ^ 2 - (x ^ 2 + 4x + 4) + 2x = 0, then x ^ 2-x-2 = 0, from the formula △ = (- 1) ^ 2-4 * 1 * (- 2) = 9, so the solution of the equation is x = 2 or x = - 2

X+5=(5X-80*2)/3

X+5=(5X-80*2)/3
3X+15=5X-160
3X-5X=-160-15
-2X=-175
X=87.5

Saw the cylinder with height of 1m into three sections, and the surface area increased by 4 square meters. What was the original volume of the cylinder in cubic meters

1 cubic meter

47 of a number is equal to the difference between 14.3 and 6.1

(14.3-6.1) △ 47, = 8.2 △ 47, = 14.35

It is known that the coefficient of quadratic term f (x) of quadratic function is a
And the solution set of inequality f (x) > - 2x is (1,3)
(1) If the function f (x) is even, find the value of A
(2) If the function g (x) = f (x) + 6A has only one zero point, find the analytic expression of F (x)
(3) If the maximum value of F (x) is a positive number, find the value range of A
Please be more detailed

(1) According to two conditions, we can get f (x) + 2x = a (x-1) (x-3), A0, and we can calculate by ourselves,

It can be made up of four different numbers: 1, 2, 3 and 4______ Four digits without repetition

Enumeration: the number of thousand is 1 is 12341243234413421423432; the number of thousand is 2 is 213421432314234124132431; the number of thousand is 3 is 3124314314324324324324324324324324334123421; the number of thousand is 4 is 412341341324213

New operation of mathematical problem definition
Regulation: a * b = A-B + 1 / a × B
(99*97)+(97*95)+(95*93)+.+(3*1）=?

（99-97+1/99*97）+（97-95+1/97*95）+.+（3-1+1/3*1）
=（3/99*97）+（3/97*95）+.+（3/3*1）
=（1/97-1/99+1/95-1/97+.+1/1-1/3）*2/3
=（1-1/99）*2/3
=49/33

Rewrite the following equation into proportion: (1) 3 * 40 = 8 * 15 (2) 2.5 * 4 = 0.5 * 2

(1)3*40=8*15
120=120
1：1
(2)2.5*4=0.5*2
10=1
10：1