Question

$8 {x}^{2} - x = 0 \\ \\ 2. {x }^{2} - 6x = 0$
Resuelve y verifica
Ayuda por favor se los pido :( doy corona a quien me ayude por favor ​

Answer 1

Explicación paso a paso:

Hallemos las raices de las cuadráticas.

$8 {x}^{2} - x = 0 \\ \\ 8( {x}^{2} - \frac{x}{8} ) = 0 \\ \\ 8( {x}^{2} - \frac{x}{8} + \frac{1}{256} - \frac{1}{256}) = 0 \\ \\ 8 ({(x - \frac{1}{16} )}^{2} - \frac{1}{256} ) = 0 \\ \\ 8 {(x - \frac{1}{16} )}^{2} - \frac{8}{256} = 0 \\ \\ 8{(x - \frac{1}{16} )}^{2} - \frac{1}{32} = 0 \\ \\ 8 {(x - \frac{1}{16} }^{2} ) = \frac{1}{32} \\ \\ {(x - \frac{1}{16} )}^{2} = \frac{1}{256} \\ \\ \sqrt{ {(x - \frac{1}{16} )}^{2}} = \sqrt{ \frac{1}{256} } \\ \\ x - \frac{1}{16} = \frac{ + }{} \frac{1}{16 } \\ \\ x = \frac{ + }{} \frac{1}{16 } + \frac{1}{16} \\ \\ x_{1} = \frac{1}{16} + \frac{1}{16} = \frac{2}{16} \\ \\ x_{2} = - \frac{1}{16} + \frac{1}{16} = 0$

Verificación:

$x_{2} = 0 \\ \\ 8 \times {(0)}^{2} + (0) = \\ 0 + 0 = \\ 0 \\ \\ x_{1} = \frac{2}{16} \\ \\ 8 \: {( \frac{2}{16} )}^{2} - \frac{ 2 }{16} = \\ \\ 8(\frac{4}{256} ) - \frac{2}{16} = \\ \\ \frac{32}{256} - \frac{2}{16} = \\ \\ \frac{2}{16} - \frac{2}{16} = 0$

${x}^{2} - 6x = 0 \\ \\ {x }^{2} - 6x+ 9 - 9 = 0 \\ \\ {(x - 3)}^{2} - 9 = 0 \\ \\ {(x - 3)}^{2} = 9 \\ \\ \sqrt{{(x - 3)}^{2} } = \sqrt{9} \\ \\ x - 3 = \frac{ + }{} 3 \\ \\ x = \frac{ + }{} 3 + 3 \\ \\ x_{1} = 3 + 3 = 6 \\ \\ x_{2} = - 3 + 3 = 0$

Verificación:

$x_{1} = 6 \\ \\ {(6)}^{2} - 6(6) = \\ 36 - 36 = \\ 0 \\ \\ \\ x_{2} = 0 \\ \\ {(0)}^{2} - 6(0) = \\ 0 + 0 = \\ 0$