Questions about one dimensional quadratic equations. Trouble master! Hurry, hurry

Solution: In the form of an +bn + c, it can be matched into a(n+b 2a) +4ac-b ) 4a, and the square term in front can determine n, such as a<0, a(n+b 2a) has a maximum value of 0, (if and only if n=-b 2a, etc.), so that the n value can be determined, and then the whole can be determined.

The recipe can also be thought of as a quadratic function, where the maximum or minimum value is obtained at the point of the axis of symmetry.

The final result of the matching method is: (x+a) +b, the square of the front can only be greater than or equal to 0, to make the result the smallest, only the square can be equal to 0, there can be an x= a, in the end, it doesn't matter if you find n or not, because the minimum number is b, of course, if there are other conditions it is different (obviously the current situation is not).

This is a quadratic function, and its curve is a parabola, symmetrical with respect to the straight line x b (2a), if it is equal to a number (0, 1, 2...).), the function changes, but the axis of symmetry does not change, the intersection point of the axis of symmetry and the function is the extremum of the function (a 0 minimum, a 0 maximum), and the extreme coordinates are {[ b (2a)], f[ b (2a)]} so this can be used to find the extremum. The formula you said, after the matching, do not need to be substituted to the original formula, with the formula a(n h) 2 k, its extreme coordinates are extremely (h, k).

One infected infected another 8 units in one round, 9 (9 1) units were infected after one infection, and after the second infection, these 9 units were infected with 8 * 9 = 72 units, plus the original 9 units, a total of 81 (9 2) units were infected, and after three infections, these 81 units were infected 81 * 8 = 648 units, plus the original 81 units, a total of 729 units (9 3), more than 700 units.

According to Veda's theorem, m=xy=k 2-4k-1=(k-2) 2-5, so the minimum value of m satisfying the condition is -5

a(1-x)-2*root2)*bx+c(1+x)=0 is organized into (c-a)x -(2*root2)*bx+(a+c)=0 with a solution, then there is [(2*root: 2)*b] -4(c-a)(a+c)>=0 to a +b -c >=0(1).

And by a, b, c are the three sides of the RT triangle abc, c=90, there is a + b -c =0, so the inequality (1) takes the equal sign, so the equation (c-a) x -(2 * root number 2) * bx + (a + c) = 0 has two equal real roots, i.e. x1 = x2

From x1+x2=12, we can get x1=x2=6, from Vedic theorem to get two equations, and then substitute x=6 into the equation (c-a)x-(2*root number 2)*bx+(a+c)=0 to get the third equation, and solve the above three equations about a, b, and c to get a, b, c

I found the value of x.

x = 6 3 times root number 2

I think this is calculated, and the rest should be easy to calculate, and the other = b -4ac = 8b -4 (c -a) = 4b to get 2b with the root number

Therefore x = (b*root2 b) (c - a).

sqrt refers to the square square.

2)(2+sqrt(6)) Kuanqing ruler 3,(2-sqrt(6)) 33) no solution completion.

6) 1+sqrt(10),1-sqrt(10)7), which is higher than the general equation ax 2+bx+c=0(a is not equal to 0)x=(-b+sqrt(b 2-4*a*c)) 2a, (-b-sqrt(b 2-4*a*c)) 2a

If b 2-4*a*c<0, then there is no solution to the equation.

2) No solution. 3) No solution.

5)-2 Quarrel 3, -4

6)1+/-sqrt(10)

7) Method: There is a solution to the sub-brigade to solve the spring solution factor or use the root formula, and there is no solution to judge the dismantling resistance.

16（x^2-x）=15

16[(x-1/2)^2-1/4]=5

16(x-1/2)^2=9

x-1 rubber2) 2=9 16

x-1/2=+ 3/4

x=5 masking 4 or x=-1 beam and destroying 4

Question 2 x=1 3+ -6 1 2 ) 3

（1）（x+1）²≥0，2（x+1）²≥0，2（x+1）²+1＞0，2x²+4x+3＞0；

2) Subtract x -x+6=(x-1 2) +23 4 0, and the value of polynomial 3x -5x-1 is always greater than the value of 2x -4x=7.

Proof: (1) 2x 4x 2 x 1 2 2x 4x 3 2 x 1 1 again x 1 0 2 x 1 0 2 x 1 1 0

Sorry, I didn't understand the second question.

Let task A be x and task B be y

Column equation: x+y=500;

x(1+10%)+y(1+20%)=570 and then solve the equation to get:

x=300y=200

So: x(1+10%)=330

y(1+20%)=240

Let A make x and B make y.

x+y=500

x（1+10%）+

y（1+20%）=570

That's how it goes. Then the column is wrong.

Overbirth, you will be counted as overbirth.

Otherwise, this kind of problem is very wrong.

If you don't understand, you can ask. Hope.