Question

[Умоляю!]
Решите систему неравенств на фото!
Даю (100) баллов!

Answer 1

Пусть x = 3k, y = 3m. Тогда

$left { {{2*(3k)^2+4*3k*3m+11*(3m)^2leq 1} atop {4*3k+7*3mgeq 3}} right. \left { {{18k^2+36km+99m^2leq 1} atop {4k+7mgeq 1}} right. \left { {{18k^2+36km+99m^2leq 1} atop {16k^2+56km+49m^2geq 1}} right. \left { {{18k^2+36km+99m^2leq 1} atop {-16k^2-56km-49m^2leq -1}} right. Rightarrow 18k^2-16k^2+36km-56km+99m^2-49m^2leq 1-1\2k^2-20km+50m^2leq 0\k^2-10km+25m^2leq 0\(k-5m)^2leq 0 Leftrightarrow k-5m=0\k=5m$

$left { {{18*(5m)^2+36*5m*m+99m^2leq 1} atop {4*5m+7mgeq 1}} right. \left { {{450m^2+180m^2+99m^2leq 1} atop {20m+7mgeq 1}} right. \left { {{729m^2leq 1} atop {27mgeq 1}} right. left { {{m^2leqfrac{1}{729} } atop {mgeq frac{1}{27}}} \right. \left { {{-frac{1}{27}leq mleqfrac{1}{27}} atop {mgeqfrac{1}{27}}} right.Rightarrow m=frac{1}{27}, k=5m=frac{5}{27}\x=3k=frac{5}{9}, y=3m=frac{1}{9}$

Ответ: $(frac{5}{9};frac{1}{9})$