Question

rezolvati in R ecuatiiile a (2x+1) (x+1) = (x-2) (2x+5)
b) (x-1) (x+1) = x la a doua +2(x-3)
c) (4x-3)ori x= (-2x+0,5) totul la a doua

Answer 1

$a)(2x + 1)(x + 1) = (x - 2)(2x + 5)$

$2 {x}^{2} + 2x + x + 1 = 2 {x}^{2} + 5x - 4x - 10$

${2x}^{2} + 3x + 1 - 2 {x}^{2} - 5x + 4x + 10 = 0$

$2x + 11 = 0$

$2x = - 11$

$x = - \frac{11}{2}$

$x = - 5.5$

$b)(x - 1)(x + 1) = {x}^{2} + 2(x - 3)$

${x}^{2} - 1 = {x}^{2} + 2x - 6$

${x}^{2} - {x}^{2} - 2x = - 6 + 1$

$- 2x = - 5 \: | \times ( - 1)$

$2x = 5$

$x = \frac{5}{2}$

$x = 2.5$

$c)(4x - 3) \times x = {( - 2x + 0.5)}^{2}$

$4 {x}^{2} - 3x = 4 {x}^{2} - 2x + 0.25$

$4 {x}^{2} - 3x - 4 {x}^{2} + 2x = 0.25$

$- x = 0.25 \: | \times ( - 1)$

$x = - 0.25$