Question

Rezolvati in multimea nr reale ecuzatia
$\sqrt{2x} + x = 4$
ce sa fac la el?Sa ridic la putere a 2 a sa scap de radical?​

Answer 1

Răspuns:

Sper că te-am putut ajuta cu mare drag

Answer 2

$\sqrt{2x}+x=4\\ \\ \text{Notez }\,\sqrt{2x} = t \Rightarrow 2x = t^2 \Rightarrow x = \dfrac{t^2}{2},\quad t \geq 0 \\ \\ \Leftrightarrow \,t + \dfrac{t^2}{2}=4\\ \\ \Leftrightarrow \,2t +t^2 =8\\ \\ \Leftrightarrow \,t^2 +2t-8 = 0\\ \\ \Delta = 4 + 32 = 36 \Rightarrow t_{1,2} = \dfrac{-2\pm 6}{2} \Rightarrow t =\dfrac{-2+6}{2}=2\geq 0 \\ \\ \Rightarrow \sqrt{2x} = 2 \Rightarrow 2x = 2^2 \Rightarrow \boxed{x = 2}$