Question

Rezolvand ecuatia 3x^2=12+6 radical 3, obtinem multimea solutiilor reale S={....}

Answer 1

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Answer 2

[tex]\it 3x^2=12+6\sqrt3 |_{:3} \Leftrightarrow x^2=4+2\sqrt3 \Leftrightarrow x^2= 1+3+2\sqrt3 \Leftrightarrow \\ \\ \Leftrightarrow x^2= 1^2+2\sqrt3 +(\sqrt3)^2 \Leftrightarrow x^2= (1+\sqrt3)^2 \Leftrightarrow \\ \\ \Leftrightarrow \sqrt{x^2} = \sqrt{(1+\sqrt3)^2} \Leftrightarrow |x| = 1+\sqrt3 \Leftrightarrow x= \pm(1+\sqrt3) \\ \\ S= \{-1-\sqrt3,\ \ 1+\sqrt3\}[/tex]