Question

resolva a equação irracional :

√6x-5=x

resp :

Answer 1

$\sqrt{6x-5}=x\\Elevando ambos os membros ao quadrado\\\\(\sqrt{6x-5})^{2}=x^{2} \\6x-5=x^{2}\\-x^{2}+6x-5=0\\[tex]X=\frac{-b+-\sqrt{b^{2}-4.a.c}}{2.a} \\X=\frac{-6+-\sqrt{6^{2}-4.(-1).(-5)}}{2.(-1)}\\X=\frac{-6+-\sqrt{36-20}}{-2}\\X=\frac{-6+-\sqrt{16}}{-2}\\X'=\frac{-6+4}{-2} = 1\\x''=\frac{-6-4}{-2} =5$