Question

Решите подстановки систему уравнений : (через Дискриминант)
Пример 3,6.
, очень нужно.

Answer 1

Объяснение:

$3) \displaystyle \left \{\begin{array}{ccc} x+y-12=0 \\\\\dfrac{1}{x} +\dfrac{1}{y} =0,375 \end{array } \right \Leftrightarrow \left \{\begin{array}{ccc} x+y=12 \\\\ \dfrac{x+y}{xy } =\dfrac{3}{8 } \end{array } \right \Leftrightarrow \left \{\begin{array}{ccc} y=12-x \\\\ 8x+8y=3xy \end{array } \right \Leftrightarrow \\\\\\ 8(12-x)+8x=3x(12-x) \\\\ 96-8x +8x=36 x-3x^2 \\\\3x^2-36x+96=0 \ \ | \div 3 \\\\ x^2-12x+32 =0 \\\\ \sf{ D} \displaystyle =12^2-32\cdot 4 =16 \\\\$

$\displaystyle x_1 =\frac{12+4}{2} =8 \ \ ; \ \ y_1 =12-8 = 4 \\\\\\ x_2 =\frac{12-4}{2} =4 \ \ ; \ \ y_2 =12-4 =8 \\\\\\ Otvet : \ \ (8 \ ; \ 4 ) \ u \ (4 \ ; \ 8 )$

$6 ) \displaystyle \left \{\begin{array}{ccc} 0,5x-y =1 \ \ | \cdot 2 \\\\ \!\!\!\!\!\!\!\!\dfrac{1}{x} -\dfrac{1}{y}=- \dfrac{1}{3} \end{array } \right \Leftrightarrow \left \{\begin{array}{ccc} x-2y =2 \\\\\dfrac{y-x}{xy }=-\dfrac{1}{3} \end{array } \right \Leftrightarrow \left \{\begin{array}{ccc} x =2+2y \\\\ 3x-3y =xy \end{array } \right \Leftrightarrow \\\\\\ 3(2+2y)-3y =(2+2y)y \\\\ 6+6y -3y =2y +2y^2 \\\\ 2y^2-y -6 =0 \\\\ \sf D= 1+4\cdot2\cdot 6 = 49$

$\displaystyle y_ 1=\frac{1+7}{4} =2 \ \ ; \ \ x_1 =2+2\cdot 2= 6 \\\\\\\ y_2=\frac{1-7}{4} =-1,5 \ \ ; \ \ x_2 = 2+(-1,5)\cdot 2=-1 \\\\\\ Otvet : (6 \ ; \ 2) \ u \ (-1 \ ; \ -1,5)$