Question

Все на картинке, ход решения без обьяснений

Answer 1

$\displaystyle\begin{cases}(a+2)(b+2)=18\\(a+b)(ab+1)=25\end{cases}\\\begin{cases}ab+2(a+b)=14\\(a+b)={\displaystyle\frac{25}{ab+1}}\end{cases}\\ab+\frac{50}{ab+1}=14\\(ab)^2+ab+50=14ab+14\\(ab)^2-13ab+36=0\\(ab)_{1,2}=\frac{13\pm\sqrt{169-144}}{2}=\frac{13\pm5}{2}\\ab=4;ab=9\\a+b=5\ \ \ \ \ \ \ \ a+b=2.5\\a=5-b\ \ \ \ \ \ \ \ a=2.5-b\\(7-b)(b+2)=18\ \ \ \ \ \ \ \ \ \ \ (4.5-b)(b+2)=18$

$\displaystyle7b+14-b^2-2b=18\ \ \ \ \ \ 4.5b+9-b^2-2b=18\\b^2-5b+4=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b^2-2.5b+9=0\\b=1;b=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b\in\varnothing\\a=4;a=1$

Ответ:

$\displaystyle\frac{a}{b}=4$