Giải phương trình: [tex](\sqrt{2-x}+1)(\sqrt{x+3}-\sqrt{x-1})=4[/tex]
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[tex](\sqrt{2-x}+1)(\sqrt{x+3}-\sqrt{x-1})=4[/tex]
[tex]\Leftrightarrow (\sqrt{2-x}+1)\frac{x+3-x+1}{\sqrt{x+3}+\sqrt{x-1}}=4[/tex]
[tex]\Leftrightarrow (\sqrt{2-x}+1)\frac{4}{\sqrt{x+3}+\sqrt{x-1}}=4[/tex]
[tex]\Leftrightarrow \frac{\sqrt{2-x}+1}{\sqrt{x+3}+\sqrt{x-1}}=1[/tex]
[tex]\Leftrightarrow \sqrt{2-x}+1=\sqrt{x+3}+\sqrt{x-1}[/tex]
[tex]\Leftrightarrow \sqrt{2-x}-1=\sqrt{x+3}-2+\sqrt{x-1}[/tex]
[tex]\Leftrightarrow \frac{2-x-1}{\sqrt{2-x}+1}=\frac{x+3-4}{\sqrt{x+3}+2}+\sqrt{x-1}[/tex]
[tex]\Leftrightarrow \frac{x-1}{\sqrt{2-x}+1}+\frac{x-1}{\sqrt{x+3}+2}+\sqrt{x-1}=0[/tex]
[tex]\Leftrightarrow\sqrt{x-1}.(\frac{\sqrt{x-1}}{\sqrt{2-x}+1}+\frac{\sqrt{x-1}}{\sqrt{x+3}+2}+1)=0[/tex]
CM trong ngoặc > 0 [tex]\Rightarrow x=1[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
