Question

Cómo se factorisa la expresión?

Answer 1

$Resolvemos : \\ \\ 2^{x-3} + 2^{x+1}+ 2^{x} = \dfrac{25}{2} \\ \\ Factorizamos\ el\ "2". \\ \\ 2^{x-3}(2^{4} + 2^{3}+1}) = \dfrac{25}{2} \\ \\ 2^{x-3}( 25) = \dfrac{25}{2} \\ \\ El\ 25\ pasa\ a\ divir. \\ \\ 2^{x-3} = \dfrac{ \dfrac{25}{2}}{\dfrac{25}{1}}\\ \\ \\ 2^{x-3} = \dfrac{\not{25}*1}{2*\not{25}}\\ \\ 2^{x-3} = \dfrac{1}{2} \\ \\ \not{2}^{x-3} = (\not{2})^{-1} \\ \\ x - 3 = - 1 \\ \\ x = - 1 + 3 \\ \\ \boxed{\boxed{x=2}}$