Question

daca vreti ma ajutati daca nu nu

Answer 1

$\it a)\ \ 40\%\ din\ a=60\%\ din\ b\ \Rightarrow\ \dfrac{40}{100}\cdot a=\dfrac{60}{100}\cdot b\ \Rightarrow\ 0,4a=0,6b|_{\cdot5}\ \Rightarrow\\ \\ \ \Rightarrow\ 2a=3b\ \Rightarrow\ \dfrac{a}{3}=\dfrac{b}{2}\ \Rightarrow\ \{a,\ \ b\}\ d.\ p.\ \{3,\ \ 2\}$

$\it b)\ \ a^2-b^2=3125\ \ \ \ \ \ (*)\\ \\ 2a=3b\ \Rightarrow\ (2a)^2=(3b)^2\ \Rightarrow\ 4a^2=9b^2|_{-4b^2}\ \Rightarrow\ 4(a^2-b^2)=5b^2\stackrel{(*)}{\Longrightarrow}\\ \\ \ \Rightarrow\ 4\cdot3125=5b^2|_{:5}\ \Rightarrow\ b^2=4\cdot625=2^2\cdot25^2\ \Rightarrow\ b=2\cdot25=50\\ \\ b=50\ \c{s}i\ 2a=3b\ \Rightarrow\ 2a=3\cdot50|_{:2}\ \Rightarrow\ a=3\cdot25=75$

Numerele cerute sunt:   a = 75,  b = 50