Question

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Задание во вложеинии

Answer 1

$begin{cases} frac1x+frac1y=5\ frac1{x^2}+frac1{y^2}=13 end{cases}Rightarrow begin{cases} frac1x=5-frac1y\ left(5-frac1yright)^2+frac1{y^2}=13 end{cases}\ left(5-frac1yright)^2+frac1{y^2}=13\ 25-frac{10}y+frac1{y^2}+frac1{y^2}=13\ frac{10}y-frac2{y^2}=12\ frac{10y-2}{y^2}=12\ 10y-2=12y^2\ 12y^2-10y+2=0\ D=100-4cdot12cdot2=4\ y_1=1,;y_2=frac23\ begin{cases} frac1x=4\ y=1 end{cases}quadquadquad begin{cases} frac1x=frac72\ y=frac23 end{cases}$

$begin{cases} x=frac14\ y=1 end{cases}quadquadquad begin{cases} x=frac27\ y=frac23 end{cases}\ OTBET:;left(frac14;;1right),;left(frac27;;frac23right)$