Question

14. Encuentra las soluciones de las siguientes ecuaciones.
a) x2+x+5= 4x + x2-2
b) -2x2 + 7 = -2x? - 1+x
c) 7x2+2=5x2 +10+2x2
d) 12x² +4 = 2(6x²+x+7)

Answer 1

Explicación paso a paso:

a)

${x}^{2} + x + 5 = 4x + {x}^{2} - 2 \\ {x}^{2} - {x }^{2} + x - 4x + 5 - 2 = 0 \\ - 3x + 3 = 0 \\ - 3x = - 3 \\ 3x = 3 \\ x \=\frac{3}{3 } \\ x = 1$

$- 2 {x}^{2} + 7 = -2 {x}^{2} - 1 + x \\ - 2 {x}^{2} + 2 {x}^{2} - x + 7 + 1 = 0 \\ - x + 8 = 0 \\ x = - 8$

$7 {x}^{2} + 2 = 5 { x }^{2} + 10 + 2 {x}^{2} \\ 7 {x}^{2} + 2 = 7 {x}^{2} + 10 \\ 7 {x}^{2} - 7 {x}^{2} + 2 - 10 = 0$

$12 {x}^{2} + 4 = 2(6 {x}^{2} + x + 7) \\ 12 {x}^{2} + 4 = 12 {x}^{2} + 2x + 14 \\ 12 {x}^{2} - 12 {x}^{2} - 2x + 4 - 14 = 0 \\ - 2x - 10 = 0 \\ 2x + 10 = 0 \\ 2x = - 10 \\ x = \frac{ - 10}{2} \\ x = - 5$

Espero te sirva.