Thank you for the process of finding math problems in the second year of junior high school

1. Move the term first, so that there is only one root sign on the left side of the equal sign; Then square the left and right at the same time, so that there is no root number on the left side of the equal sign, and there is only one root number on the right; Simplify the equation so that the equal sign is a number on one side and a root number on the other; Squaring again, you can disarm x.

2. The method is the same as the first question, but it is simpler.

3. moving items; Square; simplified equation (a root on the left, a fraction on the right); re-squaring; multiply the left and right times by the least common multiple of the denominator at the same time; You will be able to solve it.

Solution: (1) (4x+1)=5-2 (x+5) squared by: 4x+1=25-20 (x+3)+4x+12

Shift: 20 (x+3)=36

squared: x+3=81 25

x=6/25

2) The square of both sides gets: x 2+3x+4=1+2 (x 2+3x+2)+x 2+3x+2

Shift: 1=2 (x 2+3x+2).

squared: x 2 + 3x + 2 = 1 4

Solution: x=(-3 2) 2

3) Shift: [x-8) (x-5)]=2 [1 (x-5)]-1 squared: (x-8) (x-5)=4 (x-5)-4 [1 (x-5)]+1

Shift: 4 [1 (x-5)]=7 (x-5)squared:49 (x-5) 2=16 (x-5)Simplify: x=129 16

Move the two roots to both sides, then square, then move the ones with the roots to one side, and move the ones without the roots to the side, and then square them, and that's it.

Question 1: It is not possible to use factoring, but it can be solved by formula: x=(-1+-root number 13)a 4;

Question 2: b 2-4ac<0, get m>3 8;So the smallest integer is 1;

Question 3: The total area minus 570 is 70; Set the road width to x; So there is 20*2x+32x=70, and we get x=35 36;

1 。4(x2-a2) = (x-a)2 equations.

3x 2 + 2ax - 5a 2 = 0 Using the cross method, we get:

3x+5a)(x-a)=0

x=a or x= -5a3

Question 3: Solution: Let the width of the path be x, 32-2x)(20-x)=570

solution, x1=1

x2=35 (does not fit the topic, discard).

A: The path is 1 meter wide.

This is a one-time function, let y=kx+b substitute two points (,64)(2,60) to get k=-20 b=100, so y=-20x+100

The inverse proportional relationship decreases because x increases and y decreases.

1) There is no inverse theorem, its inverse proposition is false.

2) is that if the high line at the bottom of the triangle and the bisector at the top of the triangle coincide with each other, then the triangle is an isosceles triangle. (According to the "corner corners", the congruence of the left and right triangles can be proved, and the two "waists" of the triangle can be seen to be equal.) ）

Hope it helps!