Question

aflati numerele x si y, stiind ca sunt invers proportionale cu numerele 2 si 3 si ca x la puterea 2 + x la puterea 2= 208

Answer 1

[tex]\{x,y\}i.p.\{2,3\}\Rightarrow \dfrac{x}{\frac{1}{2}}=\dfrac{y}{\frac{1}{3}}=k\Rightarrow x=\dfrac{k}{2},y=\dfrac{k}{3}\\ x^2+y^2=208\\ \dfrac{k^2}{4}+\dfrac{k^2}{9}=208|\cdot 36\\ 9k^2+4k^2=7488\\ 13k^2=7488\\ k^2=576\Rightarrow k\in \{\pm 24\}\\ Pt.\ k=24\Rightarrow (x,y)=(12,8)\\ Pt.\ k=-24\Rightarrow (x,y)=(-12,-8)\\ S:(x,y)\in \{(12,8);(-12,-8)\}[/tex]