Question

Sa se rezolve in Z ecuatia 25x^2+5xy=y+2 .
Multumesc!

Answer 1

[tex] 25x^2-5xy=y+2 \ \textless \ =\ \textgreater \ (5x)^2-(5x)y=y+2\\ Notam~5x~cu ~z~si~ecuatia ~devine:\\ z^2-zy=y+2\ \textless \ =\ \textgreater \ z^2=-2=y(z+1) \ \textless \ =\ \textgreater \ y= \frac{z^2-2}{z+1} \\ y= \frac{z^2-1-1}{z+1}- \frac{1}{z+1} \\\\y = \frac{z^2-1}{z+1}- \frac{1}{z+1} \\\\ y = \frac{(z+1)(z-1)}{z+1}- \frac{1}{z+1} \\\\ \boxed{y=z-1- \frac{1}{z+1} }[/tex]