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Car11men
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1.Daca x, y ∈ R, x+y=17 si [tex] x^{2} - y^{2} [/tex] = 85 , determinati valorile lui x si y.

Răspuns :

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

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

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