Question

Система$x^{3} + y^{3} =7 x^{3} y^{3} =-9$

Answer 1

$left { {{ x^{3}+y^{3}=7} atop {x^{3}y ^{3}=-9}} right.Rightarrow left { {{y^{3} =7- x^{3} } atop { x^{3}cdot(7-x ^{3}) =-9}} right.$

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)