Система[latex] x^{3} + y^{3} =7 x^{3} y^{3} =-9[/latex]

[latex] \left \{ {{ x^{3}+y^{3}=7} \atop {x^{3}y ^{3}=-9}} \right.\Rightarrow \left \{ {{y^{3} =7- x^{3} } \atop { x^{3}\cdot(7-x ^{3}) =-9}} \right. [/latex] x³(7-x³) =-9 7x³-x⁶+9=0, x⁶-7x³-9=0, x³=t x⁶=t² t²-7t-9=0 D=(-7)²-4·(-9)=28+36=64 t₁=(7-8)/2=-1/2    или   t₂=(7+8)/2=7,5 x³ = - 1/2         или    х³ = 7,5 х₁ = - ∛(1/2)    или    х₂ = ∛(7,5)