(x+3)(x+7)=0
x 1=-3 x2=-7
x*-x- 1=0
x *-x- 1+ 1.25 = 0+ 1.25
(x-0.5)*= 1.25
x-0.5= √ 1.25
x 1 =√ 1.25+0.5 x2 =-√ 1.25+0.5
? 3x*+6x-4=0
△=b? ﹣4ac=36+48=84
x=[-b √(b? -4ac)]/2a=(-6 √84)/6
x 1 =(-6+√84)/6 x2 =(-6-√84)/6
3x(x+ 1)=3x+3
3x*+3x-3x-3=0
3x*-3=0
3(x*- 1)=0
x 1=- 1 x2= 1
4x*-4x+ 1=x*+6x+9
4x*-4x+ 1-x*-6x-9=0
3x*- 10x-8=0
(x-4)(3x+2)=0
x 1=4 x2=-3/2
7x*-√6x-5=0
△=b? ﹣4ac=6+ 140= 146
x=[-b √(b? -4ac)]/2a=(√6 √ 146)/2
? x 1=(√6-√ 146)/2
? x2=(√6+√ 146)/2
2. let the smaller one be x? The other is x+2.
x(x+2)= 168
x*+2x- 168=0
(x- 12)(x+ 14)=0
x 1= 12 x2=- 14
When x is 12, x+2= 14.
When x is-14, x+2=- 12.
The two even numbers are 12, 14 or-12 and-14 respectively.
3. Let one side be X and the other side be14-X.
? x( 14-x)÷2=24
14x-x* =48
x*- 14+48=0
? (x-6)(x-8)=0
x 1=6? x2=8
When x is 6, 14-x=8.
When x is 8, 14-x=6.
∴ becomes 8,6 at two right angles.
4. For small branches, let each branch be x long.
? 1+x+x*=9 1
? x+x*=90
x*+x-90=0
(x-9)(x+ 10)=0
? x 1=9? X2=- 10 (not in conformity with the meaning of the question, omitted)
∴ Each branch is a twig with a length of 9.
5. Let one diagonal line be x cm and the other line be 10-x cm.
? x( 10-x)÷2= 12
10x-x*-24=0
x*- 10+24=0
△=b? ﹣4ac= 100-96=4
? x=[-b √(b? -4ac)]/2a=( 10 2)/2
x 1=4? x2=6
Diagonal lines of diamonds are 4cm and 6cm respectively.
The side length of a diamond is √ (4/2) *+(6/2) * = √ 4+9 = √13 √ 3.6.
C diamond =4×3.6= 14.4.
6.? * * * There are X teams participating in the competition.
? x(x- 1)=90
? x*-x-90=0
(x- 10)(x+9)=0
X 1= 10 x2=-9 (omitted).
* * * There are 10 teams participating.