Question

1) Se considera multimea A={-1/2;radical0,(4);0,5;-radical 2 7/9; radical12}. 2) Determinati numerele reale x si y, stiind ca x la 2 + y la 2 - 6radical3x+ 4radical5y + 47=0. Va rog :P

Answer 1

2) x la 2 + y la 2 - 6radical3x+ 4radical5y + 47=0

x^2 + y^2 -6√3x +4√5y +47 = 0

[tex]\it x^2+y^2-6\sqrt3x+4\sqrt5y+47=0 \\\;\\ (x^2 -6\sqrt3x+27) + (y^2+4\sqrt5y+20 )=0 \\\;\\ (x^2 -2\cdot3\sqrt3x+(3\sqrt3)^2) + (y^2+2\cdot2\sqrt5y+(2\sqrt5)^2 )=0 [/tex]

[tex]\it (x-3\sqrt3)^2 + (y+2\sqrt5)^2=0 \Rightarrow \begin{cases} \it x-3\sqrt3=0\Rightarrow x = 3\sqrt3 \\ \\ \it y+2\sqrt5=0 \Rightarrow y= -2\sqrt5 \end{cases}[/tex]