Question

помогите пожалуйста​

Answer 1

$left { {{9^{-x}-9^{-y}=-frac{2}{9}} atop {3^{x+y}=3sqrt3}} right.; left { {{3^{-2x}-3^{-2y}=-frac{2}{9}} atop {3^{x+y}=3^{3/2}} right.; left { {{3^{-2x}-3^{-2y}=-frac{2}{9}} atop {x+y=3/2}} right. ; left { {{3^{-2x}-3^{2x-3}+frac{2}{9}=0} atop {y=3/2-x}} right.\\\a); ; frac{1}{3^{2x}}-frac{3^{2x}}{3^3}+frac{2}{9}=0\\t=3^{2x}>0; ; ,; ; frac{1}{t}-frac{t}{27}+frac{2}{9}=0; ,; ; frac{27-t^2+6t}{27t}=0; ,\\t^2-6t-27=0; ,; ; t_1=-3<0; (!); ,; t_2=9; ; (teorema; Vieta)$

$3^{2x}=9; ; to ; ; 3^{2x}=3^2; ; to ; ; 2x=2; ,; ; x=1\\b); ; y=frac{3}{2}-x=frac{3}{2}-1=frac{1}{2}\\Otvet:; ; (1, ,, frac{1}{2}); .$