Tìm x biết ( nhanh nhanh ạ em cần lắm r sáng mai em phải nộp r ạ)

Đáp án+Giải thích các bước giải:

`b)` `(x - 2)(x^2 + 2x + 7) + 2(x^2 - 4) - 5(x - 2) = 0`

`=>(x - 2)(x^2 + 2x + 7) + 2(x - 2)(x + 2) - 5(x - 2) = 0`

`=>(x - 2) [ (x^2 + 2x + 7) + 2(x + 2) - 5 ] = 0`

`=>(x - 2) [ x^2 + 2x + 7 + 2x + 4 - 5 ] = 0`

`=>(x - 2) [ x^2 + 4x + 6 ] = 0`

`=> x - 2 = 0` hoặc `x^2 + 4x + 6 = 0`

*`TH1:` `x - 2 = 0 => x = 2`

*`TH2:` `x^2 + 4x + 6 = 0`

`=>x^2 + 4x + 4 + 2 = 0`

`=>(x + 2)^2 + 2 = 0`

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

`\text{Vì` `(x + 2)^2 >= 0 AA x` 

`\text{Mà` `-2<0`

`\text{Nên` `(x+2)^2=-2` `\text{(vô lý)`

`\text{Vậy` `x = 2.`

`d)` `x^3(x^2 - 9) - 8(x^2 - 9) = 0`

`=>(x^2 - 9)(x^3 - 8) = 0`

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

`=> x - 3 = 0` hoặc `x + 3 = 0` hoặc `x - 2 = 0` hoặc `x^2 + 2x + 4 = 0`

*`TH1:` `x - 3 = 0 => x = 3`

*`TH2:` `x + 3 = 0 => x = -3`

*`TH3:` `x - 2 = 0 => x = 2`

*`TH4:` `x^2 + 2x + 4 = 0`

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

`=>(x + 1)^2 + 3 = 0`

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

`\text{Vì` `(x + 1)^2 >= 0 AA x` 

`\text{nên` `(x + 1)^2 = -3` `\text{(vô lý).`

`\text{Vậy` `x in {3; -3; x = 2}.`

`f)` `x^2(2x + 15) + 4(2x + 15) = 0`

`=>(2x + 15)(x^2 + 4) = 0`

`=> 2x + 15 = 0` hoặc `x^2 + 4 = 0`

*`TH1:` `2x + 15 = 0 => 2x = -15 => x = -15/2`

*`TH2:` `x^2 + 4 = 0 => x^2 = -4` 

`\text{Vì` `x^2 >= 0` 

`\text{nên` `x^2 = -4` `\text{(vô lý)`

`\text{Vậy` `x = -15/2.`

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

`=>2x + 6 - x^2 - 3x = 0`

`=>-x^2 - x + 6 = 0`

`=>x^2 + x - 6 = 0`

`=>x^2 + 3x - 2x - 6 = 0`

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

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

`=> x + 3 = 0` hoặc `x - 2 = 0`

`=> x = -3` hoặc `x = 2.`

`j)` `4x^2 - (x + 4)^2 = 0`

`=>(2x)^2 - (x + 4)^2 = 0`

`=>(2x - (x + 4))(2x + (x + 4)) = 0`

`=>(2x - x - 4)(2x + x + 4) = 0`

`=>(x - 4)(3x + 4) = 0`

`=> x - 4 = 0` hoặc `3x + 4 = 0`

`=>x = 4` hoặc `x = -4/3.`

`l)` `9(4x + 3)^2 = 16(3x - 5)^2`

`=>(3(4x + 3))^2 = (4(3x - 5))^2`

`=>(12x + 9)^2 = (12x - 20)^2`

`=>(12x + 9)^2 - (12x - 20)^2 = 0`

`=>( (12x + 9) - (12x - 20) ) ( (12x + 9) + (12x - 20) ) = 0`

`=>(12x + 9 - 12x + 20) (12x + 9 + 12x - 20) = 0`

`=>(29) (24x - 11) = 0`

`=> 24x - 11 = 0`

`=> 24x = 11`

`=> x = 11/24.`

`n)` `x^2 = 3x`

`=>x^2 - 3x = 0`

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

`=> x = 0` hoặc `x - 3 = 0`

`=> x = 0` hoặc `x = 3.`

`p)` `3x^3 + 9x = 0`

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

`=> 3x = 0` hoặc `x^2 + 3 = 0`

*`TH1:` `3x = 0 => x = 0`

*`TH2:` `x^2 + 3 = 0 => x^2 = -3` 

`\text{Vì` `x^2 >= 0` 

`\text{nên` `x^2 = -3` `\text{(vô lý)`

`\text{Vậy` `x = 0.`

`r)` `(2x + 5)(x - 4) = (x - 4)(x - 5)`

`=>(2x + 5)(x - 4) - (x - 4)(x - 5) = 0`

`=>(x - 4) [ (2x + 5) - (x - 5) ] = 0`

`=>(x - 4) [ 2x + 5 - x + 5 ] = 0`

`=>(x - 4)(x + 10) = 0`

`=> x - 4 = 0` hoặc `x + 10 = 0`

`=> x = 4` hoặc `x = -10.`

`t)` `(4x - 1)(x - 2) = (4x - 1)^2`

`=>(4x - 1)(x - 2) - (4x - 1)^2 = 0`

`=>(4x - 1) [ (x - 2) - (4x - 1) ] = 0`

`=>(4x - 1) [ x - 2 - 4x + 1 ] = 0`

`=>(4x - 1) ( -3x - 1 ) = 0`

`=> 4x - 1 = 0` hoặc `-3x - 1 = 0`

*`TH1:` `4x - 1 = 0 => 4x = 1 => x = 1/4`

*`TH2:` `-3x - 1 = 0 => -3x = 1 => x = -1/3.`

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