Question

初二数学题？

（1.）（x-y）^2-(x+y)(x-y) (2.)[x(x^2y^2-xy)-y(x^2-x^3y)]/3x^2y
(4.) 已知2^x=4^y+2,27^y=3^x-1,求x-y的值？

Answer 1

1.(x-y）^2-(x+y)(x-y)
=x²-2xy+y²-x²+y²
=2y(y-x)
2.[x(x^2y^2-xy)-y(x^2-x^3y)]/3x^2y
=[(x³y²-x²y)-（x²y-x³y²)]／3x²y
=2x²y（xy-1)／3x²y
=2(xy-1)／3
3.已知2^x=4^y+2
取以2为底对数： x=2(y+2) (1)
已知27^y=3^x-1
取以3为底对数：3y=x-1 (2)
(1)+(2): y=3, x=10
x-y的值: 10-3=7

Answer 2

（1.）（x-y）²-(x+y)(x-y)
=x²-2xy+y²-x²+y²
=-2xy+2y²

(2.)[x(x²y²-xy)-y(x²-x³y)]/3x²y
=(x³y²-x²y-x²y+x³y²)/(3x²y)
=(2x³y²-2x²y)/(3x²y)
=(2xy-2)/3

(4.) 已知2^x=4^y+2,27^y=3^x-1,求x-y的值？
2^x=2^(2y+4)
所以x=2y+4 (1)
3^3y=3^(x-1)
3y=x-1 (2)
(1)代入(2)
3y=2y+4-1
y=3
x=2y+4=10
所以x-y=7

Answer 3

(x-y）^2-(x+y)(x-y)=(x-y)[(x-y)-(x+y)]=-2y(x-y)

[x(x^2y^2-xy)-y(x^2-x^3y)]/3x^2y=[x^2*y(xy-1)-x^2*y(1-xy)]/3x^2*y
=2x^2*y(xy-1)/3x^2y=2(xy-1)/3

2^x=4^y+2 2^(x-2y)=2 x-2y=1
27^y=3^x-1 3^(x-3y)=1 x-3y=log(3)1 x=3-2log(3)1, y=1-long(3)1
x-y=2-log(3)1 log(3)1表示以3为底1的对数

Answer 4

（x-y）^2-(x+y)(x-y)
=(x-y)(x-y-x-y)
=2y(y-x)

[x(x^2y^2-xy)-y(x^2-x^3y)]/3x^2y
=[x^3y^2-x^2y-x^2y+x^3y^2]/3x^2y
=[2x^3y^2-2x^2y]/3x^2y
=2xy/3-2/3
=2(xy-1)/3

2^x=4^y+2 化简得
2^(x-2y)=2 那么
x-2y=1
27^y=3^x-1化简得
3^（x-3y）=1
x-3y=0
所以x=3 y=1
x-y=2