Đáp án + Giải thích các bước giải:
`a)` `3(2x-1)(3x+1)+(2x-3)(9x-1)=0`
`<=>3(6x^2+2x-3x-1)+18x^2-2x-27x+3=0`
`<=>18x^2+6x-9x-3+18x^2-2x-27x+3=0`
`<=>36x^2-32x=0`
`<=> 4x(9x - 8) = 0`
`<=>`\(\left[ \begin{array}{l}4x=0\\9x-8=0\end{array} \right.\) `<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{8}{9}\end{array} \right.\)
Vậy `S={0;8/9}`
`b)` `(x+2)(x^2-2x+4)-x(x^2+2)=5`
`<=>x^3+8-x^3-2x=5`
`<=> 8-2x=5`
`<=>2x=3`
`<=>x=3/2`
Vậy `S={3/2}`
`c)` `3(x+2)^2+(2x-1)^2-7(x+3)(x+3)=36`
`<=>3(x^2+4x+4)+(4x^2-4x+1)-7(x^2+6x+9)=36`
`<=>3x^2+12x+12+4x^2-4x+1-7x^2-42x-63=36`
`<=>-34x-50=36`
`<=>-34x=86`
`<=>x=-86/34=-43/17`
Vậy `S={-43/17}`
`d)` `(x+3)(x+2)-(x-2)(x+5)=6`
`<=>x^2+5x+6-(x^2+5x-2x-10)=6`
`<=>x^2+5x+6-x^2-5x+2x+10=6`
`<=>2x+16=6`
`<=>2x=-10`
`<=>x=-5`
Vậy `S={-5}`
`e)` `3(2x-1)(3x-1)-(2x-3)(9x-1)=0`
`<=>3(6x^2-2x-3x+1)-(18x^2-2x-27x+3)=0`
`<=>18x^2-6x-9x+3-18x^2+2x+27x-3=0`
`<=>14x=0<=>x=0`
Vậy `S={0}`.
