A, B ve C negatif tam sayılardır.
A×B=18
B×C=24
Olduğuna göre A+B+C toplamının en büyük değeri kaçtır
A) -13
B) -24
C) -30
D) -37
E) -43
Betül_Çekiç said A, B ve C negatif tam sayılardır. A×B=18, B×C=24 Olduğuna göre A+B+C toplamının en büyük değeri kaçtır? A) -13 B) -24 C) -30 D) -37 E) -43
Answer:
Given that (A), (B), and (C) are negative integers:
-
Determine possible values for (A), (B), and (C):
- We need to find pairs ((A, B)) such that (A \times B = 18) and ((B, C)) such that (B \times C = 24).
Since (A) and (B) are negative integers:
- Possible pairs for ((A, B)):
- ((-1, -18))
- ((-2, -9))
- ((-3, -6))
- ((-6, -3))
- ((-9, -2))
- ((-18, -1))
Since (B) must also form pairs with (C) such that (B \times C = 24), we test each (B):
- When (B = -1), ((-1) \times C = 24) ⟹ (C = -24)
- When (B = -2), ((-2) \times C = 24) ⟹ (C = -12)
- When (B = -3), ((-3) \times C = 24) ⟹ (C = -8)
- When (B = -6), ((-6) \times C = 24) ⟹ (C = -4)
- When (B = -12), ((-12) \times C = 24) ⟹ (C = -2)
- When (B = -24), ((-24) \times C = 24) ⟹ (C = -1)
-
Calculate (A + B + C) for each valid solution:
-
For pairs ((A, B, C)) corresponding to valid (A \times B = 18) and (B \times C = 24):
-
((A, B, C) = ((-18, -1, -24)) ⟹ (-18 + (-1) + (-24) = -43)
-
((A, B, C) = ((-9, -2, -12)) ⟹ (-9 + (-2) + (-12) = -23)
-
((A, B, C) = ((-6, -3, -8)) ⟹ (-6 + (-3) + (-8) = -17)
-
((A, B, C) = ((-4.5, -4, -6)): Not valid as (A, B, C) must be integers.
-
((A, B, C) = ((-3, -6, -4)) ⟹ (-3 + (-6) + (-4) = -13)
-
-
Identify the maximum possible value:
- Among the valid choices, the largest value of (A + B + C) is obtained from the pair ((-3, -6, -4)):
Therefore, the correct answer is \boxed{-13}.