Question

Система x/y-y/x=15/4,2x-5y=9

Answer 1

Объяснение:

$\left \{ {{\frac{x}{y}-\frac{y}{x} =\frac{15}{4} } \atop {2x-5y=9}} \right.\ \ \ \ \left \{ {{4x^2-4y^2=15xy} \atop {(2x)^2=(5y+9)^2}} \right. \ \ \ \ \left \{ {{4x^2-4y^2=15xy} \atop {4x^2=25y^2+90x+81}} \right. \ \ \ \ \Rightarrow\\25y^2+90y+81-4y^2=7,5*(5y+9)*y\\21y^2+90y+81=37,5y^2+67,5y\\16,5y^2-22,5y-81=0\ |*2\\33y^2-45y-162=0 \\D=23409\ \ \sqrt{D}=153\\y_1=3.\ \ \ \ \Rightarrow\\2x-5*3=9\\2x-15=9\\2x=24\ |:2\\x=12.$

$y_2=-\frac{18}{11}.\\2x-5*(-\frac{18}{11})=9\\2x+\frac{90}{11} =9\ |*11\\22x+90=99\\22x=9\ |:22\\x=\frac{9}{22}.$

Ответ: (12;3)   (9/22;-18/11).