Question

СРОЧНО РЕШИТЕ ПОЖАЛУЙСТА

Answer 1

$1)\; \; \left \{ {{\frac{8}{x-y}+\frac{2}{x+y}=-4} \atop {\frac{6}{x-y}+\frac{4}{x+y}=2}} \right. \; \; Zamena:\; u=x-y\; ;\; \; v=x+y\; ;\; \; uv\ne 0\\\\\\\left \{ {{\frac{4}{u}+\frac{1}{v}+2=0} \atop {\frac{3}{u}+\frac{2}{v}-1=0}} \right.\; \; \left \{ {{\frac{4v+u+2uv}{uv}=0} \atop {\frac{3v+2u-uv}{uv}=0}} \right.\; \; \left \{ {{4v+u+2uv=0\; \; \; } \atop {3v+2u-uv=0|\cdot 2}} \right. \oplus \; \left \{ {{10v+5u=0\; \; \; } \atop {3v+2u-uv=0}} \right. \\\\\\\left \{ {{u=-2v} \atop {3v-4v+2v^2=0}} \right.\; \; \left \{ {{u=-2v} \atop {2v^2-v=0}} \right.\; \; \left \{ {{u=-2v} \atop {v(2v-1)=0}} \right.\; \; \left \{ {{u=-2v} \atop {v=\frac{1}{2}\; ,\; (v\ne 0)}} \right.$

$\left \{ {{x-y=-1} \atop {x+y=\frac{1}{2}}} \right. \; \; \left \{ {{2x=-\frac{1}{2}} \atop {2y=\frac{3}{2}}} \right.\; \; \left \{ {{x=-\frac{1}{4}} \atop {y=\frac{3}{4}}} \right. \; \; \Rightarrow \; \; \underline {\; (-\frac{1}{4}\, ,\, \frac{3}{4})\; }$

$2)\; \; \left \{ {{x^2-2y^2=7} \atop {x^2+2y^2=43}} \right. \oplus \; \left \{ {{2x^2=50} \atop {x=2}} \right. \; \left \{ {{x^2=25} \atop {2y^2=43-25}} \right. \; \left \{ {{x_{1,2}=\pm 5} \atop {2y^2=18}} \right. \; \left \{ {{x_{1,2}=\pm 5} \atop {y_{1,2}=\pm 3}} \right. \\\\Otvet:\; \; (5,3)\; ,\; (-5,3)\; ,\; (5,-3)\; ,\; (-5,-3)\; .$

$3)\; \; \left\{\begin{array}{l}5x+8y-9z=-65\\4x-10y-9z=1\\9x-y=58\end{array}\right\; (1str-2str)\; \; \left\{\begin{array}{l}5x+8y-9z=-65\\x+18y=-66\\9x-y=58\end{array}\right$

$(-9\cdot 2str+3str)\; \left\{\begin{array}{l}5x+8y-9z=-65\\x+18y=-66\\-163y=652\end{array}\right\; \left\{\begin{array}{l}-9z=-65-8y-5x\\x=-66-18y\\y=-4\end{array}\right \\\\\\\left\{\begin{array}{l}-9z=-65+32-30\\x=-66+72=6\\y=-4\end{array}\right\; \; \left\{\begin{array}{ccc}z=7\\x=6\\y=-4\end{array}\right\; \; \Rightarrow \; \; (6,-4,7)$