Question

Решите неравентсва помоги ​

Answer 1

1)

${n}^{2} - {(n + 1)}^{2} > 2 \\ {n}^{2} - ( {n}^{2} + 2n + 1) > 2 \\ {n}^{2} - {n}^{2} - 2n - 1 > 2 \\ - 2n - 1 > 2 \\ - 2n > 2 + 1 \\ - 2n > 3 \\ n < - \frac{3}{2} \\ n < - 1.5$

2)

${(1 - t)}^{2} - {t}^{2} > 3 \\ 1 - 2t + {t}^{2} - {t}^{2} > 3 \\ 1 - 2t > 3 \\ - 2t > 3 - 1 \\ - 2t > 2 \\ t < - \frac{2}{2} \\ t < - 1$

3)

${(m - 2)}^{2} - 41 < {m}^{2} \\ {m}^{2} - 4m + 4 - 41 < {m}^{2} \\ - 4m + 4 - 41 < 0 \\ - 4m - 37 < 0 \\ - 4m < 37 \\ m < - \frac{37}{4} \\m > - 9.25$

4)

${m}^{2} + 9 < {(1 - m)}^{2} \\ {m}^{2} + 9 < 1 - 2m + {m}^{2} \\ 9 < 1 - 2m \\ 2m < 1 - 9 \\ 2m < - 8 \\ m < - \frac{8}{2} \\ m < - 4$