`a)`

`(3x+4)^2 - (3x-1)(3x+1) = 49`

`=> [(3x)^2+2.3x.4+4^2] -[(3x)^2-1^2]=49`

`=> (9x^2+24x+16)-(9x^2-1)=49`

`=> 9x^2+24x+16-9x^2+1=49`

`=>(9x^2-9x^2)+24x=49-16-1`

`=> 24x = 32`

`=>x=4/3`

Vậy `x=4/3`

`b)`

`x^2-4x+4=9(x-2)`

`<=> x^2-  2.x.2+2^2 = 9 (x-2)`

`<=> (x-2)^2 = 9 (x-2)`

`<=> (x-2)^2 - 9 (x-2) =0`

`<=> (x-2) (x-2-9)=0`

`<=>(x-2)(x-11)=0`

`<=>x-2=0` hoặc `x-11=0`

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

`+)x-11=0=>x=11`

Vậy `x\in{2;11}`

`c)`

`x^2 - 25 = 3x-15`

`=> x^2 - 25 - 3x + 15 =0`

`=> x^2 - 3x -10=0`

`=> x^2 - 5x + 2x - 10=0`

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

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

`=>x-5=0` hoặc `x+2=0`

`+)x-5=0=>x=5`

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

Vậy `x\in{5;-2}`

`d)`

`(x-1)^3 + 3 (x+1)^2 = (x^2 - 2x+4)(x+2)`

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

`=> (x^3 - 3x^2 + 3x - 1) + (3x^2+6x+3) = x^3 + 2^3`

`=> x^3  - 3x^2 + 3x  - 1 + 3x^2 + 6x + 3 = x^3 + 8`

`=> x^3  - 3x^2 + 3x  - 1 + 3x^2 + 6x + 3 - x^3 - 8=0`

`=> (x^3 - x^3) + (3x^2-  3x^2) + (6x+3x) + (3-1-8)=0`

`=> 9x -6=0`

`=>9x=6`

`=>x=2/3`

Vậy `x=2/3`

Đáp án `+` Giải thích các bước giải `!`

`to` Tìm `x:`

`a)`

`(3x+4)^2-(3x-1)(3x+1) = 49`

`<=> 9x^2+24x+16-9x^2+1 = 49`

`<=> (9x^2-9x^2)+24x+(16+1) = 49`

`<=> 24x+17 = 49`

`<=> 24x = 32`

`<=> x = 4/3`

Vậy `S= {4/3}`

`b)`

`x^2-4x+4 = 9(x-2)`

`<=> (x^2-4x+4)-9(x-2) = 0`

`<=> (x-2)^2-9(x-2) = 0`

`<=> (x-2)(x-2-9) = 0`

`<=> (x-2)(x-11) = 0`

`<=>` \(\left[ \begin{array}{l}x-2=0\\x-11=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=2\\x=11\end{array} \right.\) 

Vậy `S= {2; 11}`

`c)`

`x^2-25 = 3x-15`

`<=> (x^2-25)-3x+15 = 0`

`<=> (x^2-25)-(3x-15) = 0`

`<=> (x-5)(x+5)-3(x-5) = 0`

`<=> (x-5)(x+5-3) = 0`

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

`<=>` \(\left[ \begin{array}{l}x-5=0\\x+2=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=5\\x=-2\end{array} \right.\) 

Vậy `S= {5; -2}`

`d)`

`(x-1)^3+3(x+1)^2 = (x^2-2x+4)(x+2)`

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

`<=> x^3-3x^2+3x-1+3x^2+6x+3-x^3-8 = 0`

`<=> (x^3-x^3)+(-3x^2+3x^2)+(3x+6x)+(-1+3-8) = 0`

`<=> 9x-6 = 0`

`<=> 9x = 6`

`<=> x = 2/3`

Vậy `S= {2/3}`