$#DAnh$

Bài `1.`

`a.`

`1/16x^2 - x + 4 = 0`

`x^2 - 16x + 64 = 0`

`(x-8)^2 = 0`

`x-8 = 0`

`x=8` 

Vậy `x = 8` .

`b.`

`x^3 - x^2 - x + 1 = 0 `

`(x^3-x^2)-(x-1) = 0`

`x^2(x-1)-(x-1) = 0`

`(x-1)(x^2-1) = 0`

`(x-1)(x-1)(x+1)=0`

`(x-1)^2(x+1)=0`

Có `(x-1)^2=0` hoặc `x+1=0`

`x-1=0` hoặc `x = -1`

`x= 1` hoặc `x=-1`

Vậy `x ∈ {1;-1}` .

`c.`

`(2x^3 -3)^2 - ( 4x^2 - 9 ) = 0` vô nghiệm.

`star` Sửa đề :

`(2x-3)^2 - (4x^2-9) = 0`

`(2x-3)^2 - (2x-3)(2x+3) = 0`

`(2x-3)[(2x-3)-(2x+3)] = 0`

`(2x-3)(2x-3-2x-3) = 0`

`-6(2x-3) = 0`

`2x-3=0`

`2x = 3`

`x = 3/2`

Vậy `x = 3/2` .

`d.`

`x^4 + 2x^3 - 6x - 9 = 0`

`(x^4-9)+(2x^3-6x) = 0`

`(x^2-3)(x^2+3) + 2x(x^2-3) = 0`

`(x^2-3)(x^2+3+2x) = 0`

`TH_1` :

`x^2 - 3 = 0`

`x^2 = 3`

`x = +-sqrt{3}`

`TH_2` : 

`x^2+3+2x=0`

`Delta = 2^2-4.1. 3= -8<0`

`→` Pt vô nghiệm

Vậy `x = +-sqrt{3}` .

`e.`

`2( x + 5 ) - x^2 - 5x = 0`

`2(x+5) - x(x+5) = 0`

`(x+5)(2-x) = 0`

Có `x+5=0` hoặc `2-x=0`

`x=-5` hoặc `x=2` 

Vậy `x ∈ {-5;2}` .

Bài `2.`

`a.`

`9 ( x- y )^2 - 4 ( x + 1 )^2`

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

`=` `[3(x-y)-2(x+1)][3(x-y)+2(x+1)]`

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

`=` `(x-3y-2)(5x-3y+2)`

`b.`

`(x+y)^2 - 2(x+y)+1`

`=` `(x+y)^2 - 2(x+y). 1 + 1^2`

`=` `(x+y-1)^2`