Mn giúp em với ạ, em cảm ơn: (2x +1)(x +1)(3x −2)(6x −7)+4 = 0

Bạn tham khảo nhé.

`(2x+1)(x+1)(3x-2)(6x-7)+4=0`

`<=>(2x+1)(3x-2)(x+1)(6x-7)+4=0`

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

`<=>(6x^2-x-2)(6x^2-x-7)+4=0`  `(1)`

Đặt `6x^2-x=a`

Biểu thức `(1)` khi viết lại:

`=>(a-2)(a-7)+4=0`

`<=>a^2-7a-2a+14+4=0`

`<=>a^2-9a+18=0`

`<=>a^2-3a-6a+18=0`

`<=>a(a-3)-6(a-3)=0`

`<=>(a-3)(a-6)=0`

`<=>[(a-3=0),(a-6=0):}`

`<=>[(a=3),(a=6):}`

`<=>[(6x^2-x=3),(6x^2-x=6):}`

`\text{TH1:} 6x^2-x=3`

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

`<=>6.x^2-2.6.x. 1/12+6. 1/144-6. 73/144=0`

`<=>6.(x^2-2.x. 1/12+1/144-73/144)=0`

`<=>(x-1/12)^2-73/144=0`

`<=>(x-1/12)^2=73/144`

`<=>(x-1/12)^2=(\frac{+-\sqrt{73}}{12})^2`

`<=>x-1/12=\frac{+-\sqrt{73}}{12]`

`<=>x=\frac{+-\sqrt{73}+1}{12}`

`\text{TH2:} 6x^2-x=6`

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

`<=>6.x^2-2.6.x. 1/12+6. 1/144-6. 145/144=0`

`<=>6.(x^2-2.x. 1/12+1/144-145/144)=0`

`<=>(x-1/12)^2-145/144=0`

`<=>(x-1/12)^2=145/144`

`<=>(x-1/12)^2=(\frac{+-\sqrt{145}}{12})^2`

`<=>x-1/12=\frac{+-\sqrt{145}}{12}`

`<=>x=\frac{+-\sqrt{145}+1}{12]`

Vậy `x\in{\frac{+-\sqrt{73}+1}{12};\frac{+-\sqrt{145}+1}{12]}`