Răspuns:
Explicație pas cu pas:
a/2 = b/5 = k
a = 2k
b = 5k
a*b = 360
10k^2 = 360
k^2 = 360 : 10 = 36
k1 = 6
a1 = 12
b1 = 30
_____
k2 = -6
a2 = -12
b2 = -30
[tex]\it a,\ b\ \in\mathbb{N}^*,\ \ \ ab=360\ \ \ \ \ (1)\\ \\ \\ \{a,\ b\}\ d.\ p.\ \{2,\ 5\} \Rightarrow \dfrac{a}{2}=\dfrac{b}{5} \Rightarrow 5a=2b|_{\cdot b}\Rightarrow 5ab=2b^2\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow 5\cdot360=2b^2|_{:2} \Rightarrow b^2 = 5\cdot180 \Rightarrow b^2=900 \Rightarrow b^2=30^2\Rightarrow\\ \\ \Rightarrow b=30\ \ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow a\cdot30=360|_{:30}\Rightarrow a=12\\ \\ Numerele\ \ cerute\ \ sunt\ \ a=12,\ \ b=30.[/tex]