Question

Exercitiul 2 va rog !

Answer 1

$\displaystyle a). \frac{x+1}{ \sqrt{225} } = \frac{x+3}{ \sqrt{324} } \Rightarrow \frac{x+1}{15} = \frac{x+3}{18} \Rightarrow 18(x+1)=15(x+3) \Leftrightarrow \\ \\ \Leftrightarrow 18x+18=15x+45 \Rightarrow 18x-15x=45-18 \Rightarrow 3x=27 \Leftrightarrow \\ \\ \Leftrightarrow x= \frac{27}{3} \Rightarrow \boxed{x=9}$

$\displaystyle b). \frac{x+1}{ \sqrt{144} } = \frac{2,5}{15} \Rightarrow \frac{x+1}{12} = \frac{2,5}{15} \Rightarrow 15(x+1)=12 \cdot 2,5 \Leftrightarrow \\ \\ \Leftrightarrow 15x+15=30 \Rightarrow 15x=30-15 \Rightarrow 15x=15 \Rightarrow x= \frac{15}{15} \Rightarrow \boxed{x=1}$

$\displaystyle c). \frac{ \sqrt{432} }{ \sqrt{720} } = \frac{ \sqrt{15} }{x} \Rightarrow \sqrt{432 } ~x = \sqrt{720} \cdot \sqrt{15} \Rightarrow \sqrt{432} ~x= \sqrt{10800} \Leftrightarrow \\ \\ \Leftrightarrow x= \frac{ \sqrt{10800} }{ \sqrt{432} } \Rightarrow x= \sqrt{25} \Rightarrow \boxed{x=5}$

$\displaystyle d). \frac{ \sqrt{400} }{x} = \frac{ \sqrt{225} +2^4-6}{3^3-3^2-3} \Rightarrow \frac{20}{x}= \frac{15+16-6}{27-9-3} \Rightarrow \frac{20}{x} = \frac{31-6}{18-3} \Leftrightarrow \\ \\ \Leftrightarrow \frac{20}{x} = \frac{25}{15} \Rightarrow 20 \cdot 15=x \cdot 25 \Rightarrow 300=25x \Rightarrow x= \frac{300}{25} \Rightarrow \boxed{x=12}$