Question

$Am~uitat~cum~se~faceau:\\ \\ \sqrt[5-x]{x+1} =\sqrt[x]{3x-1}.\\ \\ Calculati~x.$

Answer 1

$\displaystyle Ordinul~unui~radical~este~un~numar~natural~cel~putin~egal~cu~2. \\ \\ Deci~5-x~si~x~sunt~naturale~si \ge 2. \\ \\ 5-x \ge 2 \Leftrightarrow x \le 3. \\ \\ Si~mai~avem~x \ge 2. \\ \\ Deci~x \in \{2,3\},~si~trebuie~sa~le~verificam! \\ \\ x=3~convine. \\ \\ x=2~nu~convine~(pentru~ca~am~avea~ \sqrt[3]{3}= \sqrt{5},~care,~prin \\ \\ ridicare~la~puterea~a~6-a~ar~fi~9=125,~fals). \\ \\ Solutie:~x=3.$

Answer 2

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