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Several math problems in junior high school
1. Decomposition factor: x4y-x2y3+x3y2-xy4 = x2y [x2-y2]+xy2 [x2-y2].

=xy[x^2-y^2][x+y]

=xy[x+y]^2[x-y]

Second, multiple-choice questions:

1, given 2x 2-3xy+y 2 = 0 (xy ≠ 0), the value of x/y+y/x is

2 . 3/2

b、2

two-thirds

d、9

[2x-y][x-y]=0

y=2x,x/y+y/x=5/2

y=x,x/y+y/x=2

2. Given that A 2+B 2+C 2-2 (A+B+C)+3 = 0, the value of A 3+B 3+C 3-3 ABC is

Answer, 0

b 、-3

c、3

d、9

a^2+b^2+c^2-2(a+b+c)+3=0

a^2+b^2+c^2-2a-2b-2c+3=0

a^2-2a+ 1+b^2-2b+ 1+c^2-2c+ 1=0

(a- 1)^2+(b- 1)^2+(c- 1)^2=0

a= 1,b= 1,c= 1

a^3+b^3+c^3-3abc=0

Option: a

3. It is known that the speed of a car from A to B is V 1 and the speed of returning from B to A is V2, so the original average speed of this car is

a 、( V 1+V2)/2

b 、( V 1+V2)/V 1V2

c、V 1V2/(V 1+V2)

d、2V 1V2/(V 1+V2)

2s/[s/v 1+s/v2]= 2v 1 v2/[v 1+v2]

Option: d

3. Calculation:1/x+1/2x+1/3x =?

=[6+3+2]/6x

= 1 1/6x