Question

Sa se determine multimea A={x∈R : radica din (x+3) + radical din (9-x^2) = radical de ordin 3 din (x^2+18) - 3 }

Answer 1

$\rm \sqrt{9-x^2}~este~de.fi.nit~daca~ x^{2} \leq 9,~deci~x \in [-3;3]. \\ \\ \sqrt{x+3}+ \sqrt{9-x^2} \geq 0 \Rightarrow \sqrt[3]{x^2+18} -3 \geq 0. \\ \\ \sqrt[3]{x^2+18} \geq 3 \\ x^2+18 \geq 27 \\ x^{2} \geq 9 \Rightarrow x \in (- \infty;-3 ] ~sau~x \in [3;+ \infty). \\ \\ Dar~x \in [-3;3],~de~unde~rezulta~ca~x \in \{-3;3 \}. \\ \\ Verificam~fiecare~caz~in~parte~si~obtinem~solutia~unica~x=-3.$

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