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jaroslavemelch
@jaroslavemelch
May 2021
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решить неравенство [tex] (\frac{1}{2}) x^{2} -2x \leq \frac{1}{8} [/tex]
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MizoriesKun
(1/2)х²-2х≤ 1/8 домножим обе части на 8
4х²-16х ≤ 1
4х²-16х-1≤0
D= 256+16= 272 √D=√(16*17)= 4√17
x₁=(16+4√17)/8= 2+(1/2)√17
x₂=(16-4√17)/8 = 2-(1/2)√17
+ - +
-----------+----------------------+-----------
2-(1/2)√17 2+(1/2)√17
x∈[2-(1/2)√17 ; 2+ (1/2)√17]
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Answers & Comments
4х²-16х ≤ 1
4х²-16х-1≤0
D= 256+16= 272 √D=√(16*17)= 4√17
x₁=(16+4√17)/8= 2+(1/2)√17
x₂=(16-4√17)/8 = 2-(1/2)√17
+ - +
-----------+----------------------+-----------
2-(1/2)√17 2+(1/2)√17
x∈[2-(1/2)√17 ; 2+ (1/2)√17]