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         <title><![CDATA[PROBLEME REZOLVATE]]></title>
        <description><![CDATA[&Icirc;n această categorie sunt prezentate, cu titlu gratuit,&nbsp;probleme&nbsp;av&acirc;nd&nbsp;detaliate toate&nbsp;etapele de rezolvare, cu menirea&nbsp;de a ilustra sugestiile&nbsp;din categoria &quot;CUM ABORDĂM O PROBLEMĂ&quot;.&Icirc;n plus, pot fi găsite aici şi unele referiri la modul de g&acirc;ndire al rezolvitorului, &icirc;n procesul de identificare a pistei care duce la soluţie, precum şi&nbsp;comentarii privind&nbsp;alte variante posibile.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;]]></description>
        <link>http://www.profesoronline.ro/probleme_rezolvate.html?axBA2064xABexBA83</link>
        <lastBuildDate>Wed, 17 Mar 2010 21:36:31 +0200</lastBuildDate>
        <pubDate>Wed, 17 Mar 2010 21:36:31 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-12]]></title>
					<description><![CDATA[Suport teoretic:Probabilitatea reuniunii de evenimente, probabilitatea evenimentului contrar, evenimente echiprobabile, evenimente independente.Enunt:Se arunca un zar de 3 ori si se cere probabilitatea aparitiei cel putin o data a fetei cu 2 puncte.Raspuns:$latex p=##frac{91}{216}.$]]></description>
					<link>http://www.profesoronline.ro/problema12/</link>
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					<pubDate>Wed, 10 Feb 2010 10:52:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-11]]></title>
					<description><![CDATA[Suport teoretic:Ecuatia generala a planului, plane perpendiculare, ecuatie cu 2 necunoscute in multimea numerelor naturale.Enunt:Sa se afle parametrii naturali m si n, astfel incat planele&nbsp;(p): mx - my - (n+6)z + 2 = 0&nbsp; si (q): (m-1)x - ny + z - 3 =0sa fie perpendiculare.Raspuns:$latex ...]]></description>
					<link>http://www.profesoronline.ro/problema-11.html?axBA2064xABdxBA2364xABbxBAartDet</link>
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					<pubDate>Mon, 08 Feb 2010 20:07:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-10]]></title>
					<description><![CDATA[Suport teoretic: Ecuatie cu doua necunoscute in multimea numerelor intregi, divizibilitatea in multimea numerelor intregi.Enunt:Sa se rezolve in&nbsp;multimea numerelor intregi ecuatia: $latex (2x + 4y + 1)(x - 1) = 2x.$Raspuns:&nbsp;x = 3, y = - 1.&nbsp;]]></description>
					<link>http://www.profesoronline.ro/problema-10.html?axBA2064xABdxBA2351xABbxBAartDet</link>
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					<pubDate>Tue, 26 Jan 2010 11:32:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-9]]></title>
					<description><![CDATA[Suport teoretic: Patrulater convex, patrat inscris in cerc, hexagon regulat inscris in cerc.Enunt:Sa se afle aria patrulaterului convex ABCD,&nbsp;inscris in cercul C(O;R), in&nbsp;care$latex m(##widehat{BAD})=##frac{5##pi}{12},$ (AB) este latura patratului inscris, iar (BC)&nbsp;este latura hexa...]]></description>
					<link>http://www.profesoronline.ro/problema-9.html?axBA2064xABdxBA2350xABbxBAartDet</link>
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					<pubDate>Mon, 25 Jan 2010 14:47:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-8]]></title>
					<description><![CDATA[Suport teoretic: Extremele unei functii, asimptote, rolul derivatei intai in studiul functiilor,&nbsp;bisectoarea intai.Enunt:&nbsp;Se da functia: $latex {f}:{{##mathbb{R}##setminus{##begin{Bmatrix}1##end{Bmatrix}}}}##rightarrow{##mathbb{R}},$ $latex f(x)=##frac{{x}^{2}+ax+1}{x-1}.$ Sa se afle ex...]]></description>
					<link>http://www.profesoronline.ro/problema-8.html?axBA2064xABdxBA2349xABbxBAartDet</link>
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					<pubDate>Sun, 24 Jan 2010 23:52:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-7]]></title>
					<description><![CDATA[Suport teoretic: Cardinalul unei multimi, numere rationale.Enunt:Sa se determine cardinalul multimii:$latex M=##{x##in{##mathbb{Q}}|x=##frac{n^2+2}{n^2+n},##;n=##overline{1,100}##}.$Raspuns:Card(M)=98.]]></description>
					<link>http://www.profesoronline.ro/problema7/</link>
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					<pubDate>Sun, 24 Jan 2010 23:26:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-6]]></title>
					<description><![CDATA[Suport teoretic: Formula termenului general al binomului lui Newton, ecuatie exponentiala, ecuatie de gradul al doilea.&nbsp;Enunt:$latex Se##;da##;binomul:##;{({{2}^{##frac{x}{3}} +{2}^{##frac{1-x}{2}})}^{n}}.$&nbsp; Sa se afle numarul natural nenul n si&nbsp;numarul real x, stiind ca suma ultim...]]></description>
					<link>http://www.profesoronline.ro/problema-6.html?axBA2064xABdxBA2347xABbxBAartDet</link>
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					<pubDate>Sun, 24 Jan 2010 22:56:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-5]]></title>
					<description><![CDATA[Suport teoretic: Schema lui Horner,&nbsp;ecuatie trigonometrica neomogena, ecuatie algebrica de grad superior, cu coeficenti intregi.Enunt:Sa se rezolve in multimea numerelor reale ecuatia: $latex 5{cos^4}x-{sin^3}x##cdot{cosx}-7{sin^2}x##cdot{cos^2}x+3{sinx}##cdot{cos^3}x+1=0.$Raspuns:&nbsp;$lat...]]></description>
					<link>http://www.profesoronline.ro/problema5/</link>
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					<pubDate>Sun, 24 Jan 2010 21:05:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-4]]></title>
					<description><![CDATA[Suport teoretic: Graficul unei functii, puncte comune, radacini reale, rolul derivatei in studiul functiilor.Enunt:Se dau functiile $latex f,g:{##mathbb{R}}##rightarrow{##mathbb{R}},##;unde$ $latex f(x)=24arctgx##;si##;g(x)=4x^3.$ $latex Sa##;se##;afle##;Card({{(G_f)}##cap{(G_g)}}),##;unde$&nbsp;...]]></description>
					<link>http://www.profesoronline.ro/problema-4.html?axBA2064xABdxBA2345xABbxBAartDet</link>
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					<pubDate>Sun, 24 Jan 2010 20:45:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-3]]></title>
					<description><![CDATA[Suport teoretic:Ecuatie transcendenta, solutiile unei ecuatii, functiile sinus si cosinus, functia de gradul al doilea, variatia unei functii.Enunt:Sa se arate ca ecuatia $latex {{sin}^2}{x}-(x^2-2x+4){sinx}+{cosx}=0,##;unde##;x##in{[##frac{##pi}{6},##frac{##pi}{3}]},$admite un numar par de solut...]]></description>
					<link>http://www.profesoronline.ro/problema-3.html?axBA2064xABdxBA2341xABbxBAartDet</link>
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					<pubDate>Thu, 21 Jan 2010 21:40:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-2]]></title>
					<description><![CDATA[Suport teoretic:Functie multiforma, restrictia unei functii de gradul al doilea la un anumit interval, funcţie de grad cel mult doi, functie bijectiva, inversa unei functii bijective.Enunt:Se da functia: $latex f:{##mathbb{R}}##rightarrow{##mathbb{R}},$$latex f(x)=##begin{cases}x^2+2mx-1,##;{x}#...]]></description>
					<link>http://www.profesoronline.ro/problema-2.html?axBA2064xABdxBA2340xABbxBAartDet</link>
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					<pubDate>Thu, 21 Jan 2010 21:36:00 +0200</pubDate>
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					<title><![CDATA[PROBLEMA-1]]></title>
					<description><![CDATA[Suport teoretic:Cardinalul unei multimi, imaginea unei functii, functia radical, functia sinus, functii compuse, functie bine definita.Enunt:Sa se determine cardinalul multimii Imf, unde $latex f:{##mathcal{D}}##rightarrow{##mathbb{R}},##;f(x)=##sqrt{{sin}(##frac{{##pi}x}{6})},$domeniul $latex ##...]]></description>
					<link>http://www.profesoronline.ro/problema-1.html?axBA2064xABdxBA2339xABbxBAartDet</link>
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					<pubDate>Thu, 21 Jan 2010 21:30:00 +0200</pubDate>
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