Question

8 - 9 классы. Срочно! №95. Хотя бы один пример. Пожалуйста!!! Фотография прикреплена.

Answer 1

$left { {{2x^2-3xy-19y^2=25, |cdot (-10)} atop {x^2-6y^2=250}} right. oplus left { {{2x^2-3xy-19y^2=25y=2} atop {-19x^2+30xy+184y^2=0}} right. \\19x^2-30xy-184y^2=0; |:y^2; (yne 0)\\19cdot ( frac{x}{y})^2 -30cdot frac{x}{y}-184=0\\t= frac{x}{y} ; ,; ; 19t^2-30t-184=0\\D/4=15^2+19cdot 184=3721=61^2\\t_1= frac{15-61}{19}=-frac{46}{19}; ,; ; t_2= frac{15+61}{19}=frac{76}{19} =4\\a); ; frac{x}{y}=-frac{46}{19} ; ,; ; x=- frac{46}{19}cdot y$

$x^2-6y^2=(- frac{46y}{19})^2-6y^2= frac{2116y^2}{361}-6y^2=frac{2116-114}{361}cdot y^2= frac{2002}{361}cdot y^2\\ frac{2002}{361}cdot y^2=250; ; to ; ; y^2= frac{250cdot 361}{2002}= frac{45125}{1001}; ,\\y_{1,2}=pm frac{95sqrt5}{sqrt{1001}}=pm 95sqrt{frac{5}{1001}}$

$x=-frac{46}{19} cdot y=- frac{46}{19}cdot Big (pm 95sqrt{frac{5}{1001}} Big )=mp frac{4370}{19}cdot sqrt{frac{5}{1001}}$

$b); ; frac{x}{y} =4; ,; ; x=4y\\x^2-6y^2=(4y)^2-6y^2=16y^2-6y^2=10y^2\\10y^2=250; ; to ; ; y^2=25; ,; ; y_{3,4}=pm 5\\x=4cdot y=4cdot (pm 5)=pm 20$

$Otvet:; ; Big (mp frac{4370}{19}sqrt{frac{5}{1001}}; ;; pm 95sqrt{frac{5}{1001}}Big ); ,Big (pm 5;pm 20Big ); .$