2007-02-12T20:00:00Z https://matematicasies.com/ecuaciones-irracionales-784#comment111 2007-02-12T20:00:00Z

<p><img src='https://matematicasies.com/local/cache-TeX/04aa532a83e8e1810d1ae195c97ece91.png' style="vertical-align:middle;" width="168" height="48" alt="\sqrt{36+x} = 2 + \sqrt{x}" title="\sqrt{36+x} = 2 + \sqrt{x}"> <br>elevamos al cuadrado ambos miembros:<br> <img src='https://matematicasies.com/local/cache-TeX/618020138208d12a3e83fb09e4509397.png' style="vertical-align:middle;" width="217" height="58" alt="\left( \sqrt{36+x} \right)^2= \left( 2 + \sqrt{x} \right)^2" title="\left( \sqrt{36+x} \right)^2= \left( 2 + \sqrt{x} \right)^2"> <br> <img src='https://matematicasies.com/local/cache-TeX/ae33abf4ad967e132ce93ee67cefaa80.png' style="vertical-align:middle;" width="278" height="47" alt="36 + x = 2^2 + (\sqrt{x})^2 + 2 \cdot 2 \cdot \sqrt{x}" title="36 + x = 2^2 + (\sqrt{x})^2 + 2 \cdot 2 \cdot \sqrt{x}"> <br> <img src='https://matematicasies.com/local/cache-TeX/5a7c3bc4c83d88d7a39c23003979561c.png' style="vertical-align:middle;" width="193" height="47" alt="36 + x = 4 + x + 4 \sqrt{x}" title="36 + x = 4 + x + 4 \sqrt{x}"> <br>aislamos el radical que queda<br> <img src='https://matematicasies.com/local/cache-TeX/97d40e18496224252cf2f65a8f026c8f.png' style="vertical-align:middle;" width="193" height="47" alt="36 + x - 4 - x = 4 \sqrt{x}" title="36 + x - 4 - x = 4 \sqrt{x}"> <br> <img src='https://matematicasies.com/local/cache-TeX/d1c982e58a197aca80ca328025cad184.png' style="vertical-align:middle;" width="88" height="47" alt="32 = 4 \sqrt{x}" title="32 = 4 \sqrt{x}"> <br> <img src='https://matematicasies.com/local/cache-TeX/689c179be3759e098efb23701d7bd94c.png' style="vertical-align:middle;" width="70" height="47" alt="8 = \sqrt{x}" title="8 = \sqrt{x}"> <br> <img src='https://matematicasies.com/local/cache-TeX/637f37a3bb2220d71e9ec377de2bc89b.png' style="vertical-align:middle;" width="73" height="50" alt="\fbox{64 = x}" title="\fbox{64 = x}"></p> <p>Podemos verificar la solución sustituyendo <img src='https://matematicasies.com/local/cache-TeX/ea5d2f1c4608232e07d3aa3d998e5135.png' style="vertical-align:middle;" width="23" height="38" alt="64" title="64"> por <img src='https://matematicasies.com/local/cache-TeX/9dd4e461268c8034f5c8564e155c67a6.png' style="vertical-align:middle;" width="17" height="30" alt="x" title="x"> en la ecuación original; así se confirma que <img src='https://matematicasies.com/local/cache-TeX/ea5d2f1c4608232e07d3aa3d998e5135.png' style="vertical-align:middle;" width="23" height="38" alt="64" title="64"> es la solución de la ecuación.</p>