Đặt [tex]\frac{1}{\sqrt{3x-2y}}=a> 0;\frac{1}{\sqrt{2x+5y}}=b> 0[/tex]
=>[tex]3a+4b=\frac{17}{6}[/tex]
và [tex]5a-2b=\frac{11}{6}[/tex]
=>[tex]5.(3a+4b)-3.(5a-2b)=26b=\frac{5.17}{6}-\frac{3.11}{6}=\frac{26}{3}[/tex]
=>[tex]b=\frac{1}{3}[/tex] (t/m đk)=> [tex]a=\frac{\frac{17}{6}-4b}{3}=\frac{\frac{17}{6}-\frac{4}{3}}{3}=\frac{1}{2}[/tex] (t/m đk)
=>[tex]\sqrt{3x-2y}=2;\sqrt{2x+5y}=3[/tex]
=>[tex]3x-2y=4;2x+5y=9[/tex]
=>[tex]3.(2x+5y)-2.(3x-2y)=19y=3.9-2.4=19[/tex]
=>[tex]y=1[/tex] =>[tex]x=\frac{4+2y}{3}=\frac{4+2}{3}=2[/tex]