Question

СРОЧНО РЕШИТЕ ПОЖАЛУЙСТА

Answer 1

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

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

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

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

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