Giải phương trình: $2(x-\sqrt{2x^2+5x-3}) = 1+x(\sqrt{2x-1}-2\sqrt{x+3})$

Giải thích các bước giải+Đáp án:

 `2(x-\sqrt{2x^2+5x-3})=1+x(\sqrt{2x-1}-2\sqrt{x+3})`  `(x>=1/2)`

`<=>2x-2\sqrt{2x^2+6x-x-3}=1+x\sqrt{2x-1}-2x\sqrt{x+3}`

`<=>2\sqrt{(2x-1)(x+3)}=2x-1+x\sqrt{2x-1}-2x\sqrt{x+3}`

Đặt: `\sqrt{2x-1}=t`  `(t>=0)`

`\sqrt{x+3}=m`  `(m>=0)`

`=>2tm=t^2+tx-2xm`

`<=>t^2+tx-2xm-2tm=0`

`<=>t(t+x)-2m(x+t)=0`

`<=>(t-2m)(t+x)=0`

`<=>`\(\left[ \begin{array}{l}t=2m\\t=-x\end{array} \right.\) 

`=>`\(\left[ \begin{array}{l}\sqrt{2x-1}=2\sqrt{x+3}\\\sqrt{2x-1}=-x\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}2x-1=4(x+3)\\2x-1=x^2\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}2x-1-4x-12=0\\x^2-2x+1=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}-2x-13=0\\(x-1)^2=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}x=-\dfrac{13}{2}(Loại) \\x=1\end{array} \right.\) 

Vậy: `S={1}`