Question

como se resuelve: 8(2-x)^2=2(8-x)^2
por favor ayuda!

Answer 1

Hola Nathalia

$\not 8( 2-x)^{2} =\not2( 8-x)^{2} ---\ \textgreater \ simplificando~tenemos: \\ \\ 4( 2-x)^{2} =( 8-x)^{2} ---\ \textgreater \ por~propiedad[( a-b)^{2} = a^{2} -2ab+ b^{2} ] \\ \\ 4[4-4x+ x^{2} ]=64-16x+ x^{2} \\ \\ 16-\not16x+4 x^{2} =64-\not16x+ x^{2} ~--\ \textgreater \ simplificar \\ \\ 16+4 x^{2} =64+ x^{2} \\ \\ 4 x^{2} - x^{2} =64-16 \\ \\ 3 x^{2} =48 \\ \\ x^{2} = \frac{48}{3}$
$x^{2} =16 \\ \\ x=+- \sqrt{16} \\ \\ x=+-4 \\ \\ \boxed{\boxed{ C.S=\{+4,-4\}}}$

==================================================
                                          Espero te sirva, saludos!!