Question

Реши систему уравнений.

Answer 1

$\left \{ {{x^{3}+y^{3}=91} \atop {x+y=1}} \right.\\\\:\left \{ {{(x+y)(x^{2}-xy+y^{2})=91} \atop {x+y=1}} \right.\\----------\\x^{2} -xy+y^{2}=91\\\\\left \{ {{y=1-x} \atop {x^{2}-x*(1-x)+(1-x)^{2}=91}} \right.\\\\\left \{ {{y=1-x} \atop {x^{2}-x+x^{2}+1-2x+x^{2}=91}} \right.\\\\\left \{ {{y=1-x} \atop {3x^{2}-3x-90=0}} \right.\\\\\left \{ {{y=1-x} \atop {x^{2}-x-30=0 }} \right.\\\\\left \{ {{y=1-x} \atop {\left[\begin{array}{ccc}x_{1}=6 \\x_{2}=-5 \end{array}\right }} \right.$

$1)\left \{ {{x=6} \atop {y=-5}} \right.\\\\2)\left \{ {{x=-5} \atop {y=6}} \right.$