Question

решите систему уравнений!
x/y+y/x=17/4
x+y=10

Answer 1

$frac{x}{y} =t \ frac{y}{x}= frac{1}{t} \ t+ frac{1}{t} = frac{17}{4} \ frac{t^2+1}t} =frac{17}{4} \ frac{t^2+1}t}-frac{17}{4}=0 \ frac{4t^2+4-17t}{4t} =0 \t neq 0 \ 4t^2+4-17t=0 \ D=(-17)^2-4*4*4=289-64=225=15^2 \ t1= frac{17+15}{2*4} =4 \ t2= frac{17-15}{2*4} = frac{1}{4} \ frac{x1}{y1} =4 \ frac{x2}{y2} =0.25 \ x1=4y1 \ 4y1+y1=10 \ 5y1=10 \ y1=2 \ x1=4*2=8 \ x2=0.25y2 \ 0.25y2+y2=10 \ 1.25y2=10 \ y2=8 \ x2=0.25*8=2$