Question

1.Daca x, y ∈ R, x+y=17 si $x^{2} - y^{2}$ = 85 , determinati valorile lui x si y.

Answer 1

x+y=17 => x= 17-y

 $x^{2}$-$y^{2}$= 85 => (x+y)(x-y)=85=>17(x-y)=85=> x-y=$\frac{85}{17}$ => 17-2y=$\frac{85}{17}$ =>2y= 17-$\frac{85}{17}$ =>y=$\frac{204}{34}$ = $\frac{102}{17}$ = 6 => x=11