Question

ecuaciones exponenciales con dos incognitas
$\left \{ {{\sqrt[x-y]{x+y} = \frac{1}{2\sqrt{3} } } \atop {(x+y)*2^{y-x} }=48} \right.$
res: (5;7)
paso a paso

Answer 1

$\textcircled{1}~~(x+y)^{\frac{1}{x-y}}=2^{-1}\cdot3^{-\frac{1}{2}}\\\\\textcircled{2}~~x+y =  2^{4+x-y}\cdot3\to (x+y)^{\frac{1}{x-y}}=2^{1+\frac{4}{x-y}}\cdot 3^{\frac{1}{x-y}}\\ \\\text{comparando}\\\\2^{-1}\cdot3^{-\frac{1}{2}}=2^{1+\frac{4}{x-y}}\cdot 3^{\frac{1}{x-y}}\\\\\textcircled{3}~~\dfrac{1}{x-y}=-\dfrac{1}{2}\to x-y=-2\\\\\text{Reemplazando }\textcircled{3}\text{ en }\textcircled{2}:\\\\\begin{cases}x-y=-2\\x+y=12\end{cases}\to (x,y)=(5,7)$