Question

решить систему уравнений x²+xy=7 (x+y)³=-8

Answer 1

x²+xy=7    x(x+y)=7   x*(-2)=7   x=-3,5
(x+y)³=-8   x+y=-2      y=-2-x              y=1,5.

Answer 2

$\left \{ {{x^2+xy=7} \atop {(x+y)^3=-8}} \right. \\ (1): \\ y= \frac{7-x^2}{x};x \neq 0 \\ (2): \\ (x+ \frac{7-x^2}{x})^3=-8 \\ ( \frac{7}{x})^3=-8 \\ 7^3=-2^3x^3 \\ x^3=- \frac{7^3}{2^3} \\ x=- \sqrt[3]{ \frac{7^3}{2^3} } \\ x=- \frac{7}{2} \\ y= \frac{7-x^2}{x}= \frac{7- \frac{49}{4} }{- \frac{7}{2} }=(- \frac{21}{4})*(- \frac{2}{7})= \\ = \frac{3}{2} \\ \left \{ {{x=-3.5} \atop {y=1.5}} \right.$