Question

numerele 2, 3 ,4 sunt invers proportionale cu a,b,c.a*b*c=1/3 aflati nr a, b ,c

Answer 1

[tex]\{2,3,4\}i.p.\{a,b,c\}\Rightarrow \dfrac{2}{\frac{1}{a}}=\dfrac{3}{\frac{1}{b}}=\dfrac{4}{\frac{1}{c}}\Rightarrow 2a=3b=4c=k\Rightarrow \\\Rightarrow a=\dfrac{k}{2}, b=\dfrac{k}{3},c =\dfrac{k}{4}\\ a\cdot b\cdot c=\dfrac{1}{3}\\ \dfrac{k}{2}\cdot \dfrac{k}{3}\cdot \dfrac{k}{4}=\dfrac{1}{3}\\ \dfrac{k^3}{24}=\dfrac{1}{3}|\cdot 24\\ k^3=8\Rightarrow \boxed{k=2}\\ a=\dfrac{k}{2}\Rightarrow \boxed{a=1}\\ b=\dfrac{k}{3}\Rightarrow \boxed{b=\dfrac{2}{3}}\\ c=\dfrac{k}{4}\Rightarrow \boxed{c=\dfrac{1}{2}}[/tex]