Question

Решите неравенства(35.11 - 35.13):
35.11.
1) (х + 8)^2 – х^2< 11x;
2) х^2 - (9 – х)^2> - 2x;

Answer 1

$1) \: {(x + 8)}^{2} - {x}^{2} < 11x \\ {x}^{2} + 16x + 64 - {x}^{2} < 11x \\ 16x - 11x < - 64 \\ 5x < - 64 \\ x < - 12.8$

$2) \: {x}^{2} - {(9 - x)}^{2} > - 2x \\ {x}^{2} - (81 - 18x + {x}^{2} ) > - 2x \\ {x}^{2} - 81 + 18x - {x}^{2} > - 2x \\ 18x + 2x > 81 \\ 20x > 81 \\ x > 4.05$