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sofia13
@sofia13
October 2021
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(а+4)*(a-8)> 4(2a- 19)
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(а+4)*(a-8)> 4(2a- 19)
а^2 - 8a +4a - 32 > 8a - 76
a^2 - 8a + 4a - 32 - 8a + 76 > 0
a^2 - 12a + 44 > 0
a^2 - 12 a + 44 = (a^2 - 2a * 6 + 36)- 36 +44 = (a-6)^2 + 8
(a-6)^2 + 8 > 0
Что очевидно, неравенство доказано.
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Answers & Comments
а^2 - 8a +4a - 32 > 8a - 76
a^2 - 8a + 4a - 32 - 8a + 76 > 0
a^2 - 12a + 44 > 0
a^2 - 12 a + 44 = (a^2 - 2a * 6 + 36)- 36 +44 = (a-6)^2 + 8
(a-6)^2 + 8 > 0
Что очевидно, неравенство доказано.