Question

Решите систему уравнений​

Answer 1

$left{begin{array}{l}(x-y)^2cdot |x+y|=24\frac{(x+y)^2}{|x-y|}=18end{array}right; xne y,; (x-y)^2=|x-y|^2; ,; (x+y)^2=|x+y|^2\\\left{begin{array}{l}|x-y|^2cdot |x+y|=24; ,\frac{|x+y|^2}{|x-y|}=18; ,end{array}right; ; ; u=|x-y|; ,; v=|x+y|; ; ; left{begin{array}{l}u^2cdot v=24\frac{v^2}{u}=18end{array}right$

$left{begin{array}{l}u^2v=24\v^2=18uend{array}right; ; left{begin{array}{l}v=frac{24}{u^2}\frac{24^2}{u^4}=18u}end{array}right; ; left{begin{array}{l}v=frac{24}{u^2}\u^5=32end{array}right; ; left{begin{array}{l}v=6\u=2end{array}right; ; left{begin{array}{l}|x+y|=6\|x-y|=2end{array}right$

$a)left{begin{array}{l}x+y=-6\x-y=-2end{array}right; b)left{begin{array}{l}x+y=-6\x-y=2end{array}right; c)left{begin{array}{l}x+y=6\x-y=-2end{array}right; d)left{begin{array}{l}x+y=6\x-y=2end{array}right$

$a)left{begin{array}{l}2x=-6-2\2y=-6+2end{array}right; ; left{begin{array}{l}x=frac{-6-2}{2}\y=frac{-6+2}{2}end{array}right; ; left{begin{array}{l}x=-4\y=-2end{array}right$

$b)left{begin{array}{l}2x=-6+2\2y=-6-2end{array}right; ; left{begin{array}{l}x=frac{-6+2}{2}\y=frac{-6-2}{2}end{array}right; ; left{begin{array}{ccc}x=-2\y=-4end{array}right$

$c)left{begin{array}{l}2x=6-2\2y=6+2end{array}right; ; left{begin{array}{l}x=2\y=4end{array}right$

$d)left{begin{array}{l}2x=6+2\2y=6-2end{array}right; ; left{begin{array}{l}x=4\y=2end{array}right$

$Otvet:; (-4,-2); ,; (-2,-4); ,; (2,4); ,; (4,2); .$