trung bình cộng của 2 số là 39. nếu viết thêm chữ số 7 vào bên trái số thứ nhất thì được số thứ hai. tìm hai số đó
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![](https://rs.olm.vn/images/avt/0.png?1311)
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,(3x-1) mũ 2=9/16
<=> (3x-1)^2 = ( ±3/4)^2
<=> l3x-1l = 3/4
Hoặc 3x-1 = 3/4
<=> 3x= 3/4 + 1
<=> x = 7/4 : 3
<=> x= 7/1
![](https://rs.olm.vn/images/avt/0.png?1311)
s) = ( x2 - 2xy + y2 ) - ( 2xy )2 = ( x - y - 2xy )( x - y + 2xy )
u) sửa +4y thành -4y
= 4( x - y ) - x2( x - y ) = ( x - y )( 2 - x )( 2 + x )
![](https://rs.olm.vn/images/avt/0.png?1311)
a)x²−2x−4y²−4ya)x²-2x-4y²-4y
=x²−2x−4y²−4y+2xy−2xy=x²-2x-4y²-4y+2xy-2xy
=(x²−2xy−2x)+(2xy−4y²−4y)=(x²-2xy-2x)+(2xy-4y²-4y)
=x(x−2y−2)+2y(x−2y−2)=x(x-2y-2)+2y(x-2y-2)
=(x+2y)(x−2y−2)=(x+2y)(x-2y-2)
b)x4+2x³−4x−4b)x4+2x³-4x-4
=x4+2x³+2x²−2x²−4x−4=x4+2x³+2x²-2x²-4x-4
=(x4+2x³+2x²)−(2x²+4x+4)=(x4+2x³+2x²)-(2x²+4x+4)
=x²(x²+2x+2)−2(x²+2x+2)=x²(x²+2x+2)-2(x²+2x+2)
=(x²−2)(x²+2x+2)=(x²-2)(x²+2x+2)
c)x³+2x²y−x−2yc)x³+2x²y-x-2y
=x²(x+2y)−(x+2y)=x²(x+2y)-(x+2y)
=(x²−1)(x+2y)=(x²-1)(x+2y)
=(x+1)(x−1)(x+2y)=(x+1)(x-1)(x+2y)
d)3x²−3y²−2(x−y)²d)3x²-3y²-2(x-y)²
=3(x²−y²)−2(x−y)²=3(x²-y²)-2(x-y)²
=3(x+y)(x−y)−2(x−y)²=3(x+y)(x-y)-2(x-y)²
=(x−y)[3(x+y)−2(x−y)]=(x-y)[3(x+y)-2(x-y)]
=(x−y)(3x+3y−2x+2y)=(x-y)(3x+3y-2x+2y)
=(x−y)(x+5y)=(x-y)(x+5y)
e)x³−4x²−9x+36e)x³-4x²-9x+36
=(x³−4x²)−(9x−36)=(x³-4x²)-(9x-36)
=x²(x−4)−9(x−4)=x²(x-4)-9(x-4)
=(x−4)(x²−9)=(x-4)(x²-9)
=(x−4)(x²−3²)=(x-4)(x²-3²)
=(x−4)(x+3)(x−3)=(x-4)(x+3)(x-3)
f)x²−y²−2x−2yf)x²-y²-2x-2y
=(x²−y²)−(2x+2y)=(x²-y²)-(2x+2y)
=(x+y)(x−y)−2(x+y)=(x+y)(x-y)-2(x+y)
=(x+y)(x−y−2)
hok tốt nhé
k đi
![](https://rs.olm.vn/images/avt/0.png?1311)
k) = x( 2x - 1 ) - 3y( 2x - 1 ) = ( 2x - 1 )( x - 3y )
l) = x( x - y ) + 5( x - y ) = ( x - y )( x + 5 )
m) = ( a2 - 4a + 4 )( a2 + 4a + 4 ) = ( a - 2 )2( a + 2 )2
n) = y2( x2 - 1 ) - ( x2 - 1 ) = ( x - 1 )( x + 1 )( y - 1 )( y + 1 )
q) = 3[ ( x - y )2 - 4z2 ] = 3( x - y - 2z )( x - y + 2z )
![](https://rs.olm.vn/images/avt/0.png?1311)
3^x + 4^2 = (8 - 3)^2
=> 3^x + 16 = 5^2
=> 3^x = 25 - 16
=> 3^x = 9
Mà 9 = 3^2
=> x = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
f) = x2( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )
g) = 4( x - y ) + ( x - y )2 = ( x - y )( x - y + 4 )
h) = x3( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i) = ( x - y )( x + y ) - 4( x + y ) = ( x + y )( x - y - 4 )
j) = ( x - y )( x2 + xy + y2 ) - 3( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
Trả lời:
f, x3 - 4x2 - 9x + 36 = ( x3 - 4x2 ) - ( 9x - 36 ) = x2 ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x2 - 9 ) = ( x - 4 )( x - 3 )( x + 3 )
g, 4x - 4y + x2 - 2xy + y2 = ( 4x - 4y ) + ( x2 - 2xy + y2 ) = 4 ( x - y ) + ( x - y )2 = ( x - y ) ( 4 + x - y )
h, x4 + x3 + x2 - 1 = ( x4 + x3 ) + ( x2 - 1 ) = x3 ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i, x2 - y2 - 4x - 4y = ( x2 - y2 ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )
j, x3 - y3 - 3x + 3y = ( x3 - y3 ) - ( 3x - 3y ) = ( x - y )( x2 + xy + y2 ) - 3 ( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
![](https://rs.olm.vn/images/avt/0.png?1311)
Trả lời:
a, 5x2 + 10xy + 5y2 = 5 ( x2 + 2xy + y2 ) = 5 ( x + y )2
b, x2 + 3x - y2 + 3y = ( x2 - y2 ) + ( 3x + 3y ) = ( x - y )( x + y ) + 3 ( x + y ) = ( x + y )( x - y + 3 )
c, x2 + 5x - y2 + 5y = ( x2 - y2 ) + ( 5x + 5y ) = ( x - y )( x + y ) + 5 ( x + y ) = ( x + y )( x - y + 5 )
d, 3x2 - 3y2 - 2 ( x - y )2 = 3 ( x2 - y2 ) - 2 ( x - y )2 = 3 ( x - y )( x + y ) - 2 ( x - y )2 = ( x - y )[ 3 ( x + y ) - 2 ] = ( x - y )( 3x + 3y - 2 )
e, x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2 ( x + 2y ) = ( x + 2y )( x - 2y - 2 )
a) 5x2+10xy+5y2
=5(x2+2xy+y2)
=5(x+y)2
b) x2+3x-y2+3y
=(x2-y2)+(3x+3y)
=(x-y)(x+y)+3(x+y)
=(x+y)(x-y+3)
c) x2+5x-y2+5y
=(x2-y2)+(5x+5y)
=(x-y)(x+y)+5(x+y)
=(x+y)(x-y+5)
d) 3x2-3y2-2(x-y)2
=3(x2-y2)-2(x-y)2
=3(x-y)(x+y)-2(x-y)2
=(x-y)[3(x+y)-2(x-y)]
e) x2-2x-4y2-4y
=(x2-4y2)-(2x+4y)
=(x-2y)(x+2y)-2(x+2y)
=(x+2y)(x-2y-2)
#H
Gọi 2 số đó lần lượt là a ; b
Theo bài ra ta có : \(\frac{a+b}{2}=39\left(1\right);7a=b\left(2\right)\)
(2) => \(a=\frac{b}{7}\)(3) ; (1) \(a+b=78\)(4)
Thay (3) vào (4) ta được : \(\frac{b}{7}+b=78\Leftrightarrow\frac{b+7b}{7}=\frac{546}{7}\Rightarrow8b=546\Leftrightarrow b=\frac{273}{4}\)
\(\Rightarrow a=78-\frac{273}{4}=\frac{39}{4}\)
Ooooooooooooooooooo