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Bài 4:
`a) (3x - 5)(5 - 3x) + 9(x + 1)^2 - 30`
`⇔ 15x – 9x^² – 25 + 15x + 9(x^² + 2x + 1) = 30`
`⇔ 15x – 9x^² – 25 + 15x + 9x^² + 18x + 9 = 30`
`⇔ 48x = 46`
`⇔ x = 23/24`
`b) (x + 4)^² – (x + 1)(x – 1) = 16`
`⇔ x² + 8x + 16 – x² + 1 = 16`
`⇔ 8x = -1`
`⇔ x = -1/8`
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Bài 5:
`a) A = (3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1)` và `B = 3^32 - 1`
Ta có: `B=3^32 -1`
`=(3^16 -1).(3^16 +1)`
`=(3^8 -1).(3^8 +1).(3^16 +1)`
`=(3^4 -1).(3^4 +1).(3^8 +1).(3^16 +1)`
`=(3^2 -1).(3^2 +1).(3^4 +1).(3^8 +1).(3^16 +1)`
`=(3-1).(3+1).(3^2 +1).(3^4 +1).(3^8 +1).(3^16 +1)`
`=2.(3+1).(3^2 +1).(3^4 +1).(3^8 +1).(3^16 +1) (*)`
Mà `A = (3 + 1)(3^2 + 1)(3^4 + 1)(3^8 + 1)(3^16 + 1) (**)`
Từ `(*)` và` (*) ` `=>`B = 2.A`
`=> B>A`
`b) A = 2011.2013` và `B = 2012^2`
`2011.2013 = 2011(2012 + 1) = 2011.2012 + 2011`
`2012^2 = 2012.2012 = 2012(2011 + 1) = 2012.2011 + 2012`
Ta thấy: `2011.2012 + 2011 < 2011.2012 + 2012`
`=> 2011.2013 < 2012^2`
` => A < B`
