tex]...

mathematic1 @mathematic1

June 2022 1 7 Report

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

Answers & Comments

nafanya2014

Verified answer

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

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)

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