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[basketball123]

1.GHPT:a)  $\left\{\begin{matrix} y+\sqrt{y^{2}+2y+5}=3x+\sqrt{x^{2}+4}\\ y^{2}-x^{2} +3x-3y+1=0 \end{matrix}\right.$

                      

              b)  $\left\{\begin{matrix} 3\sqrt{y-1}-\sqrt{y^{2}-6y+6}=\sqrt[3]{x+2}+1\\ y+\sqrt{y(y^{2}-3y+3)}=\sqrt[3]{x+2}+\sqrt{x+3}+1 \end{matrix}\right.$     ( Đã làm )

 

2.GPT: $5(\sqrt{4-9x^{2}}+\sqrt{2+3x}+3x)=8\sqrt{2-3x}-1$

Edited by basketball123, 03-05-2015 - 11:58.

[Vito Khang Scaletta]

2.GPT:

$5(\sqrt{4-9x^{2}}+\sqrt{2+3x}+3x)=8\sqrt{2-3x}-1$ $(1)$

Đặt $\left\{\begin{matrix} a=\sqrt{2+3x}\geq 0 \\ b=\sqrt{2-3x}\geq 0 \end{matrix}\right.\Rightarrow \left\{\begin{matrix} ab=\sqrt{4-9x^{2}} \\ \frac{a^{2}-b^{2}}{2}=3x \end{matrix}\right.$, phương trình trở thành: $5(ab+a+\frac{a^{2}-b^{2}}{2})=8b-1$

Mặc khác, ta lại có: $a^{2}+b^{2}=4$