`x^2 - 2xy - y^2 + 4xy`

`= x^2 + ( 4xy-2xy)-y^2`

`= x^2 + 2xy -y^2` `(***)`

Thay `x=1;y=2` vào `(***)` được `:`

`1^2 + 2*1*(-2) - (-2)^2`

`= -7` 

haha

`16/9 = ( 4/9 )^2` 

`( 2x - 2/3 )^2 - 1 = 7/9`

`=> ( 2x - 2/3 )^2 = 7/9+1`

`=> ( 2x - 2/3 )^2 = 16/9 = ( 4/3 )^2 = ( -4/3 )^2`

`=> 2x - 2/3 = 4/3` hoặc `2x - 2/3 = -4/3`

`=> 2x = 6/3 = 2` hoặc `2x = -2/3`

`=> x = 1` hoặc `x = -1/3`

Vậy `x in { 1;-1/3}`

`F = 7+7^2+....+7^{100}`

`=> 7F = 7^2 + 7^3+....+7^{101}`

`=> 6F = 7F - F = (  7^2 + 7^3+....+7^{101})-(7+7^2+....+7^{100})`

`=> 6F = 7^{101} - 7`

`=> 6F + 7 = 7^{101}-7+7=7^{101} = 7^n` nên `n = 101`

Vậy `n=101`

Chiều cao hình thang đó là `:`

`( 47,2 xx 2 )/( 8,6 + 7,4 ) = 5,9(m)`

$Đ/s : 5,9m$ 

Ta có `:`

`x^3 - 7x-6`

`= x^3 - 9x + 2x - 6`

`= x( x^2 - 9 ) + 2( x-3 )`

`= x( x-3 )( x + 3 ) + 2( x-3 )`

`= [ x( x + 3 )+2]( x-3 )`

`= ( x^2 + 3x + 2 )( x-3 )`

`= ( x^2 + 2x + x + 2 )( x-3 )`

`= [x( x+2 ) + ( x + 2 )]( x-3 )`

`= ( x+1)(x+2)(x-3)`  

`( 19x + 2*5^2 ) : 14 = ( 13-8)^2 - 4^2`

`=> ( 19x + 50 ) : 14 = 5^2 - 4^2`

`=> ( 19x + 50 ) : 14 = 9`

`=> 19x + 50 = 9*14`

`=> 19x + 50 = 126`

`=> x = ( 126 - 50 )/19`

`=> x = 4`

Vậy `x=4` 

`a)`

`3+5/2 = 6/2 + 5/2 = 11/2`

`b)`

`2/8 : 4/8 = 1/4 : 1/2 = 1/4 *2=1/2`

`c)`

`13/5 - 2 = 13/5 - 10/5 = 3/5`

`d)`

`1/2 xx 2/5 = 1/5`