`#0409`

Bài `11`

`a,`

`(x-2)(3x+5)=(2x-4)(x+1)`

`3x^2-x-10=2x^2-2x-4`

`x^2+x-6=0`

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

`x=-3` hoặc `x=2`

Vậy `S={-3;2}`

`b,`

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

`2x^2-3x-20=-x^2+9x-20`

`3x^2-12x=0`

`3x(x-4)=0`

`x=0` hoặc `x=4`

Vậy `S={0;4}`

`c,`

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

`9x^2-1=6x^2-7x-3`

`3x^2+7x+2=0`

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

`x=-1/3` hoặc `x=-2`

Vậy `S={-1/3;-2}`

`d,`

`2(9x^2+6x+1)=(3x+1)(x-2)`

`18x^2+12x+2=3x^2-5x-2`

`15x^2+17x+4=0`

`(3x+1)(5x+4)=0`

`x=-1/3` hoặc `x=-4/5`

Vậy `S={-1/3;-4/5}`

`e,`

`27x^2(x+3)-12(x^2+3x)=0`

`27x^2(x+3)-12x(x+3)=0`

`(27x^2-12x)(x+3)=0`

`x(27x-12)(x+3)=0`

`x=0` hoặc `x=4/9` hoặc `x=-3`

Vậy `S={0;4/9;-3}`

`f,`

`16x^2-8x+1=4(x+3)(4x-1)`

`16x^2-8x+1=4(4x^2+11x-3)`

`16x^2-8x+1=16x^2+44x-12`

`-52x+13=0`

`-52x=-13`

`x=1/4`

Vậy `S={1/4}`

Bài `12`

`a,`

`3x^2-11x+6=0`

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

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

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

`x=2/3` hoặc `x=3`

Vậy `S={2/3;3}`

`b,`

`-2x^2+5x-3=0`

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

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

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

`x=3/2` hoặc `x=1`

Vậy `S={3/2;1}`

`c,`

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

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

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

`(x+3)(x-1)=0`

`x=-3` hoặc `x=1`

Vậy `S={-3;1}`

`d,`

`x^2-4x-5=0`

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

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

`(x-5)(x+1)=0`

`x=5` hoặc `x=-1`

Vậy `S={5;-1}`

Bài `13`

`a,`

`2x^4+3x^2-5=0`

Đặt `x^2=t` `(t>=0)`

Nên phương trình trở thành `:` `2t^2+3t-5=0`

`2t^2-2t+5t-5=0`

`2t(t-1)+5(t-1)=0`

`(2t+5)(t-1)=0`

`t=-5/2` `(ktm)` hoặc `t=1` `(tm)`

Với `t=1->x^2=1->x=+-1`

Vậy `S={+-1}`

`b,`

`x^4-8x^3-9x^2=0`

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

`x^2(x-9)(x+1)=0`

`x=0` hoặc `x=9` hoặc `x=-1`

Vậy `S={0;9;-1}`

`c,`

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

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

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

`x=+-1` hoặc `x=4`

Vậy `S={+-1;4}`

`d,`

`x^4+2x^3+5x^2+4x-12=0`

`x^3(x+2)+(5x-6)(x+2)=0`

`(x+2)(x^3+5x-6)=0`

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

`(x+2)[x^2(x-1)+x(x-1)+6(x-1)]=0`

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

`x=-2` hoặc `x=1`

Vậy `S={-2;1}`