Puteri si radicali

Ana Mier Oct 10, 2012 1:27 am

Va rog frumos , spuneti-mi si mie cum se face un astfel de exercitiu:
$\sqrt{\left ( x-3 \right )^{2}} + \sqrt{\left ( y-2 \right )^{2}}=0$

Si va rog frumos sa imi explicati si acest exercitiu, va rog frumos:

$\sqrt{\frac{12}{11}+\frac{13}{22}+\frac{14}{33}+...+\frac{110}{1089}-\left ( 1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99} \right )}$

Va rog mult de tot sa imi explicati la amandoua. Multumesc! Thank You

**Admin** Mier Oct 10, 2012 7:10 pm

Problema 1:
$\begin{array}{l} \sqrt {{{\left( {x - 3} \right)}^2}} + \sqrt {{{\left( {y - 2} \right)}^2}} = 0 \Leftrightarrow \left| {x - 3} \right| + \left| {y - 2} \right| = 0\\ {\text{Am folosit proprietatea }}\sqrt {{a^2}} = \left| a \right| \ge 0\\ \bullet \underline {{\text{Teorie}}} {\text{: {\color{Red} o suma de expresii matematice pozitiva} }} = 0 \Leftrightarrow {\text{{\color{Red} fiecare expresie}}} = 0\\ \left\{ \begin{array}{l} \left| {x - 3} \right| \ge 0\\ \left| {y - 2} \right| \ge 0 \end{array} \right. \Rightarrow \left| {x - 3} \right| + \left| {y - 2} \right| = 0 \Leftrightarrow \left\{ \begin{array}{l} \left| {x - 3} \right| = 0\\ \left| {y - 2} \right| = 0 \end{array} \right. \end{array}$
Mai departe, va descurcați ?!

**Admin** Mier Oct 10, 2012 7:47 pm

Problema 2:
$\begin{array}{l} S = \frac{{12}}{{11}} + \frac{{13}}{{22}} + \frac{{14}}{{33}}... + \frac{{110}}{{1089}} - \left( {1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{99}}} \right)\\ \frac{{12}}{{11}} - 1 = \frac{{12 - 11}}{{11}} = \frac{1}{{11}}\\ \frac{{13}}{{22}} - \frac{1}{2} = \frac{{13 - 11}}{{22}} = \frac{2}{{22}} = \frac{1}{{11}}\\ \frac{{14}}{{33}} - \frac{1}{3} = \frac{{14 - 11}}{{33}} = \frac{3}{{33}} = \frac{1}{{11}}\\ ............\\ \frac{{110}}{{1089}} - \frac{1}{{99}} = \frac{{110 - 11}}{{1089}} = \frac{{99}}{{1089}} = \frac{1}{{11}}\\ S = \underbrace {\frac{1}{{11}} + ... + \frac{1}{{11}}}_{{\rm{ de 99 ori}}} = \frac{{99}}{{11}} = 9 \end{array}$

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