Răspuns:
9804
Explicație pas cu pas:
a + b + c = 31
2a + 3b + 4c = 105
2a + 3b + 4c = 105
2a + 2b + 2c = 2×31
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b + 2c = 105 - 62
=> b + 2c = 43
2a + 3b + 4c = 2a + b + 2b + 4c = (2a + b) + 2(b + 2c) = (2a + b) + 2×43 = 2a + b + 86 = 105
=> 2a + b = 19
2a + 3b + 4c = 105
3a + 3b + 3c = 3×31
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-a + c = 105 = 93
=> c - a = 12
(2a+b)(b+2c)(c-a) = 19×43×12
=> (2a+b)(b+2c)(c-a) = 9804
