Question

Кто умеет решать такие , помогите пожалуйста)

Answer 1

$1)quad left { {{10^{1+lg(x+y)}=50} atop {lg(x+y)+lg(x-y)=2-lg5}} right. ; ; ODZ:; left { {{x textgreater -y} atop {x textgreater y}} right. \\ left { {{10cdot 10^{lg(x+y)}=50} atop {lg[(x+y)(x-y)]=lg10^2-lg5}} right. ; ,; ; a^{log_{a}b}=b; to ; 10^{lgb}=b\\left { {{10^{lg(x+y)}=50:10} atop {lg[(x+y)(x-y)]=lgfrac{100}{5}}} right. ; left { {{x+y=5} atop {(x+y)(x-y)=20}} right. ; left { {{x+y=5} atop {5(x-y)=20}} right. ; left { {{x+y=5} atop {x-y=4}} right.$

$left { {{2x=9} atop {2y=1}} right. ; left { {{x=4,5} atop {y=0,5}} right. ; ; ; Otvet:; ; (4,5, ;, 0,5), .\\2)quad left { {{lgx-lgy=lg15-1} atop {10^{lg(3x+2y)}=39}} right. ; , ; ; ODZ:; ; left { {{x textgreater 0,; y textgreater 0} atop {x textgreater -frac{2y}{3}}} right. \\ left { {{lgfrac{x}{y}=lg15-lg10} atop {3x+2y=39}} right. ; left { {lgfrac{x}{y}=lgfrac{15}{10}} atop {3x+2y=39}} right. ; left { {{frac{x}{y}=frac{3}{2}} atop {3x+2y=39}} right.$

$left { {{x=frac{3y}{2}} atop {3cdot frac{3y}{2}+2y=39}} right. ; left { {{x=frac{3y}{2}} atop {frac{13y}{2}=39}} right. ; left { {{x=frac{3cdot 6}{2}=9} atop {y=frac{2cdot 39}{13}=6}} right. \\Otvet:; (9,6); .$