Question

Sendo U = R, resolva a equação irracional x = V6-x.
ajudemmmmmmmmmmmmmmmmmmmmm plis

Answer 1

$\boxed{\begin{array}{l}\sf x=\sqrt{6-x}\\\sf x^2=(\sqrt{6-x})^2\\\sf x^2=6-x\\\sf x^2+x-6=0\\\sf\Delta=b^2-4ac\\\sf\Delta=1^2-4\cdot1\cdot(-6)\\\sf\Delta=1+24\\\sf\Delta=25\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-1\pm\sqrt{25}}{2\cdot1}\\\\\sf x=\dfrac{-1\pm5}{2}\begin{cases}\sf x_1=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\\sf x_2=\dfrac{-1-5}{2}=-\dfrac{6}{2}=-3\end{cases}\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm verificac_{\!\!,}\tilde ao:}\\\sf para~x=2:\\\sf 2=\sqrt{6-2}\\\sf 2=\sqrt{4}\\\sf 2=2\checkmark\implies 2~\acute e~soluc_{\!\!,}\tilde ao.\\\sf para~x=-3:\\\sf -3=\sqrt{6-(-3)}\\\sf -3=\sqrt{6+3}\\\sf -3=\sqrt{9}\\\sf -3\ne3\implies -3~n\tilde ao~\acute e~soluc_{\!\!,}\tilde ao.\end{array}}$