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Rezolvati:

|2x+1|=5=>x € ???

X+3/2=8/x-3 => x € ??

|x+y| +y la puterea 2 -4y+4=0=>x=?? y=???


Răspuns :

[tex]|2x+1|=5=\ \textgreater \ 2x+1=5~sau~2x+1=-5. \\ 2x+1=5=\ \textgreater \ 2x=4=\ \textgreater \ \boxed{x=2}. \\ 2x+1=-5=\ \textgreater \ 2x=-6=\ \textgreater \ \boxed{x=-3}.[/tex]
Solutie: x∈{-3 ; 2}

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[tex]\frac{x+3}{2}= \frac{8}{x-3} =\ \textgreater \ (x+3)(x-3)=16\ \textless \ =\ \textgreater \ x^{2} -9=16=\ \textgreater \ x^{2} =25=\ \textgreater \ \\ =\ \textgreater \ \boxed{x=5}~sau~\boxed{x=-5}.[/tex]
Solutie: x∈:{-5 ; 5}

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[tex]|x+y|+ y^{2}-4y+4=0\ \textless \ =\ \textgreater \ |x+y|+(y-2) ^{2} =0. \\ Dar~|x+y| \geq 0~si~(y-2) ^{2} \geq 0.~Iar~cum~|x+y|+(y-2) ^{2} =0, \\ rezulta~|x+y|=0~si~(y-2) ^{2} =0. \\ (y-2) ^{2} =0=\ \textgreater \ y-2=0=\ \textgreater \ \boxed{y=2}. \\ |x+y|=0=\ \textgreater \ x+y=0\ \textless \ =\ \textgreater \ x+2=0=\ \textgreater \ \boxed{x=-2}.[/tex]
Solutie: x=-2 si y=2.