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alinkin92
@alinkin92
October 2021
1
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Решить неравенство где x в квадрате - 1 2/3 x -2/3 < 0
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evvoronina1
Х^2 - 1 2/3 • х - 2/3 < 0
х^2 - 5/3 • х - 2/3 < 0
Умножим обе части неравенства на 3:
3х^2 - 5х - 2 < 0
Дискриминант: b² - 4ac = 5^2 - 4•3•2 = 25-24=1
х1 = (5 + √1)/(2•3) = 5:6=1
х2 = (5 - √1)/(2•3) = 4/6 = 2/3
(х-1)•(х-2/3) < 0
Верно, если
х-1<0, х<1
х-2/3>0, х>2/3
Неравенство верно при 2/3 < х < 1
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Answers & Comments
х^2 - 5/3 • х - 2/3 < 0
Умножим обе части неравенства на 3:
3х^2 - 5х - 2 < 0
Дискриминант: b² - 4ac = 5^2 - 4•3•2 = 25-24=1
х1 = (5 + √1)/(2•3) = 5:6=1
х2 = (5 - √1)/(2•3) = 4/6 = 2/3
(х-1)•(х-2/3) < 0
Верно, если
х-1<0, х<1
х-2/3>0, х>2/3
Неравенство верно при 2/3 < х < 1