Mathematics 9th grade Help solve the equations, thank you for the process!

Answer: 1. Factorization method: the original equation is deformed

3 x 2 x x 2 = x 2 [3 x 2 x] = x 2 2x 6 = 0, x 2 = 0 or 2x 6 = 0

x = 2 or x = 3.

2. Matching method:

y²－8y=－10，y²－8y＋4²=－10＋4²，﹙y－4﹚²=6，y－4=±√6，y=4±√6。

3. Formula method:

x=－1±½√1²＋4﹚

1.Let one of the numbers be xThen the other number is 14-x their Jiwei 45, i.e.

x(14-x)=45

14x-x^2=45

x^2-14x+45=0

x-9)(x-5)=0

x=9 or x=5

When x=9, the other number is 14-9=5

When x=5, the other number is 14-5=9

That is, these two numbers are 5 and 9

2.If the bamboo pole is x feet long, then the width of the door frame is x-4 feet. If the door frame is x-2 feet high, then there is.

x-4）^2+(x-2)^2=x^2

x^2-8x+16+x^2-4x+4-x^2=0x^2-12x+20=0

x-2)(x-10)=0

x=2 or x=10

Because x-4>0 then x>4

That is, the length of the bamboo pole is 10 feet.

3.The side length of this square vegetable garden is x meters. According to the title, 15x 2+30*4x=3600 can be obtained

15x^2+120x-3600=0

x^2+8x-240=0

x+10)(x-2)=0

x=-10 or x=2

Because x is the edge length of the vegetable garden, it cannot be negative, that is, the edge length of the vegetable garden is 2 meters4If there are x teams, then a team has x-1 opponents, so it is necessary to play (x-1)*2 games, all x*(x-1)*2=90*2

Therefore x=10

1.The product of two numbers is 45,9*5=45,9+5=14, so it is 5,9.

2.Set the length of the bamboo pole x, the width of the door frame = x-4, and the height of the door frame = x-2(x-4) 2+(x-2) 2=x 2

x1 = 7, x2 = 2, round off x2, because the height of the door frame cannot be 0, so the bamboo pole is 73 longLet the side length be x meters.

x^2*15+4x*30=3600

x1 = 20, x2 = -12, round off x2, because the side length cannot be negative, so the side length is 20 meters.

2 games were played.

x for 90 games.

2 x = 2 9090 teams.

1.Solution: x 2+6x+9=7+9 (x+3) 2=16 x+3=+-4 x1=1,x2=-7

2.Solution: 3(x+1)=2(x-1) or 3(x+1)=-2(x-1) x1=-5 or x2=-1 5

3.Solution: (y+1+3)(y+1-1)=0 y+4=0 or y=0 y1=-4 or y2=0

4.Solution: If m=-1, the original equation is -x-1=0 x=-1

If m≠-1, [(m+1)x+m](x+1)=0 (m+1)x+m=0 or x+1=0 x1=-m (m+1) or x2=-1

5.Solution: 48-x 2+4=x+2-x+2 x 2=48 x=+-4 root number 3. Upon examination, they are both roots of the original equation.

6.Solution: Let (x 2-3) x=y The original equation is y+3 y=13 2 y1=6, y2=1 2

When y=6, (x 2-3) x=6 x=3+-2 root number 3;When y=1 2, (x 2-3) x=1 2 x=2 , x=-3 2

After testing, the root of the original equation is: x1=3+2 root number 3, x2=3-root number 3, x3=2, x4=-3 2

7.Solution: x and y are the two roots of m 2-4m+5=0, and the discriminant formula =(-4) -4*1*5<0 There is no real solution to this problem.

8. Solution: Get, y=2x+1

Substitution, x 2 + x - 4 x - 2 + 4 = 0 x 1 = 1, x 2 = 2

Substitution, y1=3, y2=5

The solution of the original system of equations is.

x1=1 x2=2

y1=3 y2=5

1、x²+6x=7

x+3)²-9=7

x+3)²=16

x+3=±4

x=1 or x=-7

x+1)²-4(x-1)²=0

3(x+1)+2(x-1))(3(x+1)-2(x-1))=0(5x+1)(x+5)=0

x=-1 5 or x=-5

3、(y+1)²+2(y+1)=3

y+1)²+2(y+1)-3=0

y+1-1)(y+1+3)=0

y=0 or y=-4

4、（m+1)x²+(2m+1)x+m=0((m+1)x+m)(x+1)=0

x=-m (m+1) or x=-1

（x²-4)-1=1/(x-2)-1/(x+2)(48-x²+4)/(x²-4)=(x+2-x+2)/(x²-4)52-x²=4

x = 48x = 4 root number 3

6. (x -3) x+3x (x -3)=13 2 ream(x -3) x=y

y+3/y=13/2

2y²-13y+6=0

2y-1)(y-6)=0

y=1 2 or y=6

x -3) x = 1 2 or (x -3) x = 6 i.e. 2x -x-6 = 0 or x -6x - 3 = 0

2x+3)(x-2)=0 or (x-3)=12x=-3 2 or x=2 or x=3 2 root number 3

7. x+y=4, x=4-y

xy=5 substituting to get 4y-y =5

i.e. y -4y + 5 = 0

y-2)²+1=0

Equations have no real roots.

So there is no real solution to the system of equations.

8、x²+x-2y+4=0

2x-y+1=0, y=2x+1

Substituting it yields x + x-2 (2x + 1) + 4 = 0

x²-3x+2=0

x-1)(x-2)=0

The solution yields x=1 or x=2

Substituting yields y=3 or y=5

So the system of equations is solved as x=1, y=3 or x=2, y=5

Do this question yourself, and you will improve.

1.Let one of the searches be the number of xThen the other number is 14-x their Jiwei 45, i.e.

x(14-x)=45

14x-x^2=45

x^2-14x+45=0

x-9)(x-5)=0

x=9 or x=5

When x=9, the other number is 14-9=5

When x=5, the other number is 14-5=9

That is, these two numbers are 5 and 9

2.If the bamboo pole is x feet long, then the width of the door frame is x-4 feet. The height of the door frame is x-2 feet.

Then there is. x-4）^2+(x-2)^2=x^2x^2-8x+16+x^2-4x+4-x^2=0x^2-12x+20=0

x-2)(x-10)=0

x=2 or x=10

Because X-4>0

Then x>4

That is, the length of the bamboo pole is 10 feet.

3.The side length of this square vegetable garden is x meters. It can be obtained according to the title.

15x^2+30*4x=3600

15x^2+120x-3600=0

x^2+8x-240=0

x+10)(x-2)=0

x=-10 or x=2

Because x is the edge length of the vegetable garden, it cannot be negative.

That is, the vegetable garden is 2 meters long.

4.If there are x teams, then one team has x-1 opponents.

Therefore, it is necessary to play (x-1)*2 games.

All x*(missing x-1)*2=90*2

Therefore x=10

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