Question

Resuelve las siguientes ecuaciones completando trinomio cuadrado perfecto

Answer 1

Respuesta:

${x}^{2} - 4x + 1$

$({x}^{2} - 4x + 4 - 4 )+ 1 = 0$

${(x - 2)}^{2} - 3 = 0$

${(x - 2)}^{2} = 3$

$x = 2 + \sqrt{3} \to \: x = 2 - \sqrt{3}$

$2 {x}^{2} + 12x - 16 = 0$

Sacando mitad

${x}^{2} + 6x - 8 = 0$

$({x}^{2} + 2(3)x + 9 - 9 )- 8 = 0$

${(x + 3)}^{2} - 17 = 0$

${(x + 3)}^{2} = 17$

Toma dos valores

$x = - 3 + \sqrt{17} \to \: x = - 3 - \sqrt{17}$

${x}^{2} + 16x + 64 = 0$

${(x + 8)}^{2} = 0$

$x = 8 \to \: x = + 8$