Question

Решите неравенства 32.18

Answer 1

$1)n {}^{2} - (n {}^{2} + 2n + 1) > 2 \\ n { }^{2} - n {}^{2} - 2n - 1 > 2 \\ - 2n - 1 > 2 \\ - 2n > 2 + 1 \\ - 2n > 3 \\ n < - \frac{3}{2} \\ 2)1 - 2t + t {}^{2} - t {}^{2} > 3 \\ 1 - 2t > 3 \\ - 2t > 3 - 1 \\ - 2t > 2 \\ t < - 1 \\ 3)m {}^{2} - 4m + 4 - 41 < m {}^{2} \\ - 4m + 4 - 41 < 0 \\ - 4m - 37 < 0 \\ - 4m < 37 \\ m > - \frac{37}{4} \\ 4)m {}^{2} + 9 < 1 - 2m + m {}^{2} \\ 9 < 1 - 2m \\ 2m < 1 - 9 \\ 2m < - 8 \\ m < - 4$