Question

用简便方法计算

57.6*1.6+28.8*36.8-14.4*80
直接写出因式分解的结果:
3a^2-6a+3=_________

若|a-2|+b^2-2b+1=0 则a=_______,b=_______

如果x+y=0,xy=-7,则x^2y+xy^2=_______,x^2+y^2=________

若x^2+mx+n是一个完全平方式,则m,n的关系是_________

Answer 1

57.6*1.6+28.8*36.8-14.4*80
=14.4*4*1.6+14.4*2*36.8-14.4*80
=14.4*6.4+14.4*73.6-14.4*80
=14.4*(6.4+73.6-80)
=14.4*0
=0
直接写出因式分解的结果:
3a^2-6a+3=3(a-1)^2

若|a-2|+b^2-2b+1=0 则a=2,b=1
|a-2|+(b-1)^2=0
a-2=0,b-1=0
a=2,b=1

如果x+y=0,xy=-7,则x^2y+xy^2=0,x^2+y^2=14
x^2y+xy^2=xy(x+y)=-7*0=0
x^2+y^2=(x+y)^2-2xy=0-2*(-7)=14

若x^2+mx+n是一个完全平方式,则m,n的关系是n=(1/4)m^2
n=(m/2)^2
n=(1/4)m^2

Answer 2

57.6*1.6+28.8*36.8-14.4*80 =14.4(4*1.6+2*36.8-80)=14.4*0=0

3a^2-6a+3=3(a-1)^2

|a-2|+b^2-2b+1=|a-2|+(b-1)^2=0
a=2,b=1

如果x+y=0,xy=-7,则
x^2y+xy^2=xy(x+y)=-7*0=0
x^2+y^2=(x+y)^2-2xy=0^2-2*(-7)=14

x^2+mx+n=(x+m/2)^2+n-m^2/4是一个完全平方式,则
n-m^2/4=0
n=m^2/4

Answer 3

57.6*1.6+28.8*36.8-14.4*80
=57.6*1.6+57.6*18.4-57.6*20
=57.6*(1.6+18.4-20)
=57.6*0
=0

3a^2-6a+3=3(a-1)^2

|a-2|+b^2-2b+1=|a-2|+(b-1)^2=0
所以a-2=0 b-1=0
a=2 b=1

x^2y+xy^2=(x+y)*xy=0*(-7)=0
x^2+y^2=(x+y)^2-2xy=0-2*(-7)=14

(m/2)^2=n

Answer 4

57.6×1.6+57.6×18.4-57.6×20=57.6×40=2304
=3(a^2-2a+1)=3(a-1)^2
a-2=0,b^2-2b+1=0 a=2,b=1
x^2y+xy^2=xy(x+y)=-7×0=0 x^2+y^2=(x+y)^2-2xy=14
(m/2)^2=n

Answer 5

1 3(a-1)^2
2 a=2 b=1
3 x^2y+xy^2=0 x^2+y^2=14
4 n=m^2/4