Question

Розв'яжи систему рівнянь. Срочнооо ​

Answer 1

$\displaystyle\bf\\\left \{ {{\dfrac{4}{4x+y} +\dfrac{9}{4x-y}=7 } \atop {\dfrac{3}{4x+y} +\dfrac{8}{4x-y}=6 }} \right.$

Сделаем замену :

$\displaystyle\bf\\\frac{1}{4x+y} =a \ \ \ ; \ \ \ \frac{1}{4x-y} =b$

Получим систему :

$\displaystyle\bf\\\left \{ {{4a+9b=7} \ |\cdot 3 \atop {3a+8b=6} \ |\cdot(-4)} \right. \\\\\\+\left \{ {{12a+27b=21} \atop {-12a-32b=-24}} \right. \\------------\\-5b=-3\\\\b=\frac{3}{5} \\\\3a=6-8b=6-8\cdot\frac{3}{5}=6-\frac{24}{5}=\frac{6}{5}\\\\a=\frac{6}{5} :3=\frac{2}{5}$

Перейдём к замене :

$\displaystyle\bf\\\left \{ {{\dfrac{1}{4x+y} =\dfrac{2}{5} } \atop {\dfrac{1}{4x-y} =\dfrac{3}{5} }} \right.\\\\\\\left \{ {{2\cdot(4x+y)=5} \atop {3\cdot(4x-y)=5}} \right.\\\\\\2\cdot(4x+y)=3\cdot(4x-y)\\\\8x+2y=12x-3y\\\\2y+3y=12x-8x\\\\5y=4x\\\\y=\frac{4x}{5}=0,8x\\\\\\\frac{1}{4x+0,8x} =\frac{2}{5} \\\\\\\frac{1}{4,8x} =\frac{2}{5}\\\\\\9,6x=5\\\\x=\frac{25}{48} \\\\y=0,8\cdot\frac{25}{48} =\frac{5}{12} \\\\\\Otvet \ : \ x=\frac{25}{48} \ \ ; \ \ y=\frac{5}{12}$