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

Đáp án:

`S= {\frac{\sqrt{13}+4}{2}; \frac{-\sqrt{13}+4}{2}}`

Giải thích các bước giải:

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

`<=> 8x^2-12x = 4x^2+6x-2x-3`

`<=> (8x^2-4x^2)-(12x+6x-2x) = -3`

`<=> 4x^2-16x+3 = 0`

`<=> (4x^2-16x+16)-13 = 0`

`<=> 4(x^2-4x+4) = 13`

`<=> (x-2)^2 = 13/4`

`<=>` $\left[ \begin{array}{l}x-2 = \sqrt{\dfrac{13}{4}}\\x-2 = -\sqrt{\dfrac{13}{4}}\end{array} \right.$ 

`<=>` $\left[ \begin{array}{l}x = \dfrac{\sqrt{13}}{2}+2\\x = \dfrac{-\sqrt{13}}{2}+2\end{array} \right.$

`<=>` $\left[ \begin{array}{l}x = \dfrac{\sqrt{13}}{2}+\dfrac{4}{2}\\x = \dfrac{-\sqrt{13}}{2}+\dfrac{4}{2}\end{array} \right.$

`<=>` $\left[ \begin{array}{l}x = \dfrac{\sqrt{13}+4}{2}\\x = \dfrac{-\sqrt{13}+4}{2}\end{array} \right.$

Vậy `S= {\frac{\sqrt{13}+4}{2}; \frac{-\sqrt{13}+4}{2}}`