[latex]x+y=7 \ xy=12 \ a)x^2+y^2 \ b)x^2-y^2 \ c)x-y \ ------- \ a)(x+y)^2=x^2+y^2+2xy \ 49=x^2+y^2+24 \ oxed{x^2+y^2=25} \ b)x*y=12 \ Daca~x=1~si~y=12 Longrightarrow x+y eq 7 \ Daca~x=4~si~y=3 Longrightarrow x+y=7 => x=4~si~y=3 \ x^2-y^2=4^2-3^2 \ oxed{x^2-y^2=5} \ c)x-y=4-3 \ oxed{x-y=1}[/latex] [latex]x-y=3 \ x^2+y^2=29 \ a)xy \ b)x+y \ c)x^2-y^2 \ ------- \ a)(x-y)^2=x^2+y^2-2xy \ 9=29-2xy \ 2xy=20 \ oxed{xy=10} \ b)x*y=10 \ Daca~x=1~si~y=10 Longrightarrow x-y eq 3 \ Daca~x=5~si~y=2 Longrightarrow x-y=3~deci~x=5~si~y=2 \ x+y=5+2 \ oxed{x+y=7} \ c)x^2-y^2=5^2-2^2 \ oxed{x^2-y^2=21}[/latex]