fie a si b numerele cautate
{a,b} d.p {5,3}
[tex] b^{2} - a^{2} =64[/tex]
[tex] \frac{a}{5} = \frac{b}{3} [/tex] ridicam toata relatia la patrat
[tex] \frac{ a^{2} }{ 5^{2} } = \frac{ b^{2} }{ 3^{2} } [/tex]
[tex] \frac{ a^{2} }{25} = \frac{ b^{2} }{9} [/tex]
⇒ [tex] a^{2} = \frac{25* b^{2} }{9} [/tex]
[tex] \frac{25*b^{2} }{9} - \frac{9* b^{2} }{9} =64
[/tex]
[tex] \frac{16 *b^{2} }{9} =64[/tex]
[tex] b^{2} = \frac{64*9}{16} [/tex]
[tex] b^{2} = 36[/tex] ⇒ b=6⇒a=10
