Question

Решите систему уравнений

Х³+у³=9
Ху=2

Answer 1

Ответ:

приведено ниже:

$\left \{ {{x^3 + y^3=9} \atop {x*y=2}} \right. \\\left \{ {{\frac{8}{y^3} + y^3=9} \atop {x=\frac{2}{y} }} \right. \\\\8+y^6=9y^3\\y^6-9y^3+8=0\\t=y^3\\t^2-9t+8=0\\\\D=81-4*8=49\\t1=\frac{9-7}{2}=1\\t2=\frac{9+7}{2}=8\\\\y1=1\\y2=2\\x1=2\\x2=1$