Giải phương trình sau:
[tex]5\sqrt{x-1}-\sqrt{x+7}=3x-4[/tex]
[tex]5.\sqrt{x-1}-\sqrt{x+7}=3x-4\\\\ => 25(x-1)+(x+7)-10\sqrt{x^2+6x-7}=9x^2-24x+16\\\\ <=> 9x^2-24x+16=26x-18-10\sqrt{x^2+6x-7}\\\\ <=> 9x^2-50x+34+10\sqrt{x^2+6x-7}=0\\\\ <=> 9x^2-30x+24+10.[\sqrt{x^2+6x-7}-(2x-1)]=0\\\\ <=> 3(3x^2-10x+8)+10\frac{x^2+6x-7-(4x^2-4x+1)}{\sqrt{x^2+6x-7}+(2x-1)}=0\\\\ <=> 3.(3x^2-10x+8)+10.\frac{-3x^2+10x-8}{\sqrt{x^2+6x-7}+(2x-1)}=0\\\\ <=> (3x^2-10x+8)[3-\frac{10}{\sqrt{x^2+6x-7}+(2x-1)}]=0\\\\ *, \frac{10}{\sqrt{x^2+6x-7}+2x-1}=3\\\\ +, x>\frac{4}{3} => \sqrt{x^2+6x-7}+2x-1>\frac{10}{3}\\\\ => \frac{10}{\sqrt{x^2+6x-7}+2x-1}<3 => ....\\\\ +, x<\frac{4}{3} =>....\\\\ +, x=\frac{4}{3} =>....[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
