[tex]\displaystyle\\
x^2+y^2=290\\
xy=143\\
---\\
\text{Stim ca:}\\
(x+y)^2=x^2+2xy+y^2\\
\Longrightarrow~~x^2+y^2=(x+y)^2-2xy\\
x^2+y^2=290\\
xy=143\\
---\\
(x+y)^2-2xy=290\\
(x+y)^2=290+2xy\\
(x+y)^2=290+2\cdot 143\\
(x+y)^2=290+286\\
(x+y)^2=576\\
x+y=\sqrt{576} \\
x+y=24\\
\text{Avem ecuatiile:}\\
x+y=24\\
xy=143\\
\text{Descompunem pe 143 in factori primi:}\\
143=11\cdot13
\Longrightarrow~~\boxed{\bf x=11~si~y=13~~sau~~ x=13~si~x=11}\\
\text{Verificam suma}\\
x+y=11+13=24~~\bf Corect[/tex]
