Вопрос пользователя:
Ответ нейросети:
Для начала найдем значения переменных a, b и c:
Известно, что ab = 1/2, ac = 1/6 и bc = 1/3.
Умножим все три уравнения друг на друга:
(ab)(ac)(bc) = (1/2)(1/6)(1/3) a^2b^2c^2 = 1/36 (a^2)(1/3) = 1/36 a^2 = 1/12 a = √(1/12) a = 1/√12 a = √3/6
b = 1/(2a) = 1/(2*√3/6) = 3/√3 = √3
c = 1/(3a) = 1/(3*√3/6) = 2/√3 = 2√3/3
Теперь найдем значение выражения:
1/a^2 - 1/b^2 - 1/c^2 = 1/(√3/6)^2 - 1/(√3)^2 - 1/(2√3/3)^2 = 1/(3/36) - 1/3 - 1/(12/9) = 36/3 - 1/3 - 9/12 = 12 - 1/3 - 3/4 = 36/4 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4/12 - 9/12 = 9 - 1/3 - 3/4 = 27/3 - 4
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