Question

Stiind ca 4a-b/4a+b=2/5 aflati raportul numerelor a si b

va rog

Answer 1

$\it Fie\ \ \dfrac{a}{b}=k\ \Rightarrow\ a=bk\ \ \ \ \ \ (1)\\ \\ \\ \dfrac{4a-b}{4a+b}=\dfrac{2}{5}\ \stackrel{(1)}{\Longrightarrow}\ \dfrac{4bk-b}{4bk+b}=\dfrac{2}{5} \Rightarrow \dfrac{b(4k-1)}{b(4k+1)}=\dfrac{2}{5} \Rightarrow \dfrac{4k-1}{4k+1}=\dfrac{2}{5} \Rightarrow\\ \\ \\ \Rightarrow 20k-5=8k+2 \Rightarrow 20k-8k=2+5 \Rightarrow 12k=7 \Rightarrow k=\dfrac{7}{12}\\ \\ \\ Deci,\ \ \dfrac{a}{b}=\dfrac{7}{12}$