tex]...

July 2022 1 20 Report

Решите систему уравнений
[tex] \left \{ {{ \frac{16}{x+y}+ \frac{16}{x-y}=3 } \atop { \frac{8}{x+y}+ \frac{12}{x-y}=2 }} \right. [/tex]

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NNNLLL54

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$\left \{ {{ \frac{16}{x+y}+\frac{16}{x-y}=3 } \atop {\frac{8}{x+y}+\frac{12}{x-y}=2}} \right. \; ,\; \; u=\frac{1}{x+y}\; ,\; v=\frac{1}{x-y}\; ,\; x\ne \pm y\\\\ \left \{ {{16u+16v=3} \atop {8u+12v=2\, |\cdot (-2)}} \right. \; ,\; \left \{ {{-8v=-1} \atop {8u+12v=2}} \right. \; ,\; \left \{ {{v=\frac{1}{8}} \atop {8u+\frac{12}{8}=2}} \right. \; ,\; \left \{ {{v=\frac{1}{8}} \atop {u=\frac{1}{16}}} \right. \\\\v=\frac{1}{x-y}=\frac{1}{8}\; ,\; x-y=8\\\\u=\frac{1}{x+y}=\frac{1}{16}\; ,\; x+y=16$

$\left \{ {{x-y=8} \atop {x+y=16}} \right. \; ,\; \left \{ {{2x=24} \atop {2y=8}} \right. \; ,\; \left \{ {{x=12} \atop {y=4}} \right.$

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