Question

Bài 6: Giải các phương trình sau:

4)

12) 

Answer 1

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

`<=>6(2x-5)-10(x+3)=15(2-3x)-30x-60`

`<=>12x-30-10x-30=30-45x-30x-60`

`<=>2x-60=-30-75x`

`<=>77x=30`

`<=>x=30/77`

Vậy `S={30/77}`

`12)(x^2-3x)^2-2(x^2-3)=8`

`<=>x^4+9x^2-6x^3-2x^2+6-8=0`

`<=>x^4-6x^3+7x^2-2=0`

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

`<=>x^3(x-1)-5x^2(x-1)+2x(x-1)+2(x-1)=0`

`<=>(x-1)(x^3-5x^2+2x+2)=0`

`<=>(x-1)(x^3-x^2-4x^2+4x-2x+2)=0`

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

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

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

`<=>(x-1)(x-2-\sqrt{6})(x-2+\sqrt{6})=0`

`<=>` $\left[ \begin{array}{l}x=1\\x=2-\sqrt{6}\\x=2+\sqrt{6}\end{array} \right.$