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daca x-y=9 si xy=10, atunci x²+y²= ?

Răspuns :

Ridicam la patrat expresia x-y=9 (x-y)la patrat=81 obtinem xpatrat-2xy+ypatrat=81. Observam ca in conditie e dat ca xy=10,atunci 2xy=20 . Inlocuind obtinem xpatrat+ypatrat-20=81 , xpatrat+ypatrat=101.Sper ca ai inteles :) 
x^2+y^2=(x-y)^2+2xy=81+20=101