Question

Sa se rezolve in RxR sistemul de ecuatii$\left \{ {{x-y=1} \atop {x^{2}-y^{2}=41 }} \right.$

Answer 1

(x-y)(x+1)=41[tex] \left \{ {{x-y=1} \atop { x^{2} - y^{2} =41}} \right. [/tex] ⇒
$\left \{ {{x-y=1} \atop {(x-y)(x+y)=41}} \right.$⇒
$\left \{ {{x-y=1} \atop {x+y=41}} \right.$, adunam cela 2 ec. si avem 2x=42 I :2 ⇒  x=21, din x-y=1 ⇒21-y=1⇒y=20 deci solutia; x=21 ; y=20