2 ответа:
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Раскладываем число на множители
1)12096:4=3024
2) 3024:4=756
3) 756:4=189
4) 189:9=21
5) 21:7=3
6) 3:3=1
![\sqrt[3]{12096} = \sqrt[3]{4*4*4*9*7*3} = \sqrt[3]{4*4*4*3*3*3*7} = \sqrt[3]{4^3*3^3*7} \\ \\ =4*3 \sqrt[3]{7} =12\sqrt[3]{7}](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B12096%7D+%3D+%5Csqrt%5B3%5D%7B4%2A4%2A4%2A9%2A7%2A3%7D+%3D+%5Csqrt%5B3%5D%7B4%2A4%2A4%2A3%2A3%2A3%2A7%7D+%3D+%5Csqrt%5B3%5D%7B4%5E3%2A3%5E3%2A7%7D++%5C%5C+%5C%5C+%3D4%2A3+%5Csqrt%5B3%5D%7B7%7D+%3D12%5Csqrt%5B3%5D%7B7%7D+)
б)
1) <span>1048576:4=262144
</span>2) 262144:4=65536
3) 65536:4=16384
4) 16384:4=4096
5) 4096:4=1024
6)1024:4=256
7) 256:4=64
8) 64:8=8
9)8:8=1
![\sqrt[4]{1048576} = \sqrt[4]{4*4*4*4*4*4*4*8*8} = \\ \\ =\sqrt[4]{4^4*4^3*4*2*2^3}= \sqrt[4]{4^4*4^4*2^4}=4*4*2=32](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7B1048576%7D+%3D++%5Csqrt%5B4%5D%7B4%2A4%2A4%2A4%2A4%2A4%2A4%2A8%2A8%7D+%3D+%5C%5C+%5C%5C+%3D%5Csqrt%5B4%5D%7B4%5E4%2A4%5E3%2A4%2A2%2A2%5E3%7D%3D+%5Csqrt%5B4%5D%7B4%5E4%2A4%5E4%2A2%5E4%7D%3D4%2A4%2A2%3D32+)
1)12096:4=3024
2) 3024:4=756
3) 756:4=189
4) 189:9=21
5) 21:7=3
6) 3:3=1
б)
1) <span>1048576:4=262144
</span>2) 262144:4=65536
3) 65536:4=16384
4) 16384:4=4096
5) 4096:4=1024
6)1024:4=256
7) 256:4=64
8) 64:8=8
9)8:8=1
(x - 1)(2x - 2) < (2x - 1)(x + 2)
2x² - 2x - 2x + 2 < 2x² + 4x - x - 2
- 4x + 2 < 3x - 2
- 7x < - 4
Ответ: x ∈ (4/7 ; + ∞)
2x² - 2x - 2x + 2 < 2x² + 4x - x - 2
- 4x + 2 < 3x - 2
- 7x < - 4
Ответ: x ∈ (4/7 ; + ∞)