Question

qual o resultado da equação:

$\frac{ \sqrt{6x-4}}{3}=\frac{12} \sqrt{6x+4}$

Answer 1

$\frac{ \sqrt{6x-4} }{\sqrt{3}} = \frac{12}{ \sqrt{6x+4} } \\ \\ \sqrt{6x-4} * \sqrt{6x+4} = 12*\sqrt{3} \\ \sqrt{(6x-4)*(6x+4)} = 12*\sqrt{3} \\ \sqrt{36x^2+24x-24x-16} = 12*\sqrt{3} \\ \sqrt{36x^2-16} =12*\sqrt{3}\\ (\sqrt{36x^2-16})^2 = (12*\sqrt{3})^2 \\ 36x^2-16 = 12^2*\sqrt{3}^2 \\ 36x^2 -16 = 144*3 \\ 36x^2-16 = 432 \\ 36x^2 = 432+16 \\ 36x^2 = 448 \\ x^2 = \frac{448}{36} \\ x = \sqrt \frac{448}{36} \\ x = \frac{8 \sqrt{7} }{6} \\ x = \frac{4 \sqrt{7} }{3}$