[tex]a)\sqrt{x+3}=5-\sqrt{x-2} b)\sqrt{2x-1}-\sqrt{x+2}=x-3[/tex]
a,
ĐKXĐ : [tex]x\geq 2[/tex]
Pt => [tex]\sqrt{x+3}-3+\sqrt{x-2}-2=0[/tex]
=> [tex]\frac{x+3-9}{\sqrt{x+3}+3}+\frac{x-2-4}{\sqrt{x-2}+2}=0[/tex]
=> [tex](x-6)(\frac{1}{\sqrt{x+3}+3}+\frac{1}{\sqrt{x-2}+2})=0[/tex]
=> x=6 (vì cái trong ngoặc > 0)
b,
ĐKXĐ [tex]x\geq \frac{1}{2}[/tex]
Pt => [tex]\frac{2x-1-x-2}{\sqrt{2x-1}+\sqrt{x+2}}=x-3[/tex]
=> [tex](x-3)(\frac{1}{\sqrt{2x-1}+\sqrt{x+2}}-1)=0[/tex]
Vì [tex]x\geq \frac{1}{2}[/tex] => [tex]\sqrt{x+2}>1[/tex]
=> [tex]\frac{1}{\sqrt{2x-1}+\sqrt{x+2}}-1[/tex] khác 0
=> x=3
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
