Question

como resolver a equaçao do 2ºgrau: x²- 1/3 = 1/6x²

Answer 1

Oi Bruninha,

na equação $x^2- \dfrac{1}{3}= \dfrac{1}{6} x^2$, podemos fazer..

$\dfrac{1}{6}x^2-x^2=- \dfrac{1}{3}\\\\ \dfrac{1}{6}x^2- \dfrac{6x^2}{6}= -\dfrac{1}{3}\\\\ \dfrac{1-6}{6}x^2= -\dfrac{1}{3}\\\\ -\dfrac{5}{6}x^2=- \dfrac{1}{3} \\\\MMC(3~e~6)=6\\\\ \dfrac{1\cdot(-5)}{\not6}x^2=- \dfrac{2\cdot1}{\not6}\\\\ -5x^2=-2\\\\ x^2= \dfrac{-2}{-5}\\\\ x^2= \dfrac{2}{5}\\\\ x=\pm \sqrt{ \dfrac{2}{5} }\\\\\\ \Large\boxed{\boxed{S=\left\{ \sqrt{ \dfrac{2}{5} } ,- \sqrt{ \dfrac{2}{5} }\right\}}}$

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