Question

Помогите пожалуйста сурныч №214

Answer 1

214.

1)

$(x -1)(x + 2) > (x + 1)(x - 2)$

${x}^{2} + 2x - x - 2 > {x}^{2} - 2x + x - 2$

${x}^{2} + x - 2 > {x}^{2} - x - 2$

${x}^{2} - {x}^{2} + x + x - 2 + 2 > 0$

$2x > 0$

$x > 0$

2)

$(x + 1)(x - 8) > (x + 2)(x - 4)$

${x}^{2} - 8x + x - 8 > {x}^{2} - 4x + 2x - 8$

${x}^{2} - 7x - 8 > {x}^{2} - 2x - 8$

${x}^{2} - {x}^{2} - 7x + 2x - 8 + 8 > 0$

$- 5x > 0$

$x > 0$

3)

${(x - 3)}^{2} < (4 + x)(x - 4)$

${x}^{2} + 9 - 6x < 4x - 16 + {x}^{2} - 4x$

${x}^{2} - {x}^{2} - 6x + 4x + 9 + 16 < 0$

$- 2x < - 9 - 16$