MathSolver74
ab + c + d = 3 ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ (1)
bc + a + d = 5 ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ (2)
cd + a + b = 2 ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ (3)
da + b + c = 6 ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ (4)
(1) + (2) = (3) + (4) ab + c + d + bc + a + d = cd + a + b + da + b + c
b(a + c) + 2d = d(a + c) + 2b
(b − d)(a + c) = 2(b − d)
(b − d)(a + c − 2) = 0
b = d atau a + c = 2
• Jika b = d
Persamaan (2) bc + a + b = 5
Persamaan (3) bc + a + b
MathSolver74
Kontradiksi maka tidak ada nilai a, b, c dan d yang memenuhi.
• Jika a + c = 2
(1) + (2) ab + bc + a + c + 2d = 8
b(a + c) + a + c + 2d = 8
b + d = 3
(2) + (3) bc + cd + 2a + b + d = 7
c(b + d) + 2a + b + d = 7
3c + 2a = 4
3c + 2(2 − c) = 4 c = 0 a = 2
Persamaan (2) b(0) + (2) + d = 5 d = 3 b = 3 − (3) = 0
(a, b, c, d) yang memenuhi adalah (2, 0, 0, 3)
Maka,