SOLUSI BULAT
Persamaan
x2 – 11y2 + 23 = 10xy memiliki empat buah solusi bulat (xi
, yi). Tentukan │x1│ + │x2│ + │x3│
+ │x4│ .
A.
8
B.
40
C.
44
D.
46
E.
52
Solusi
Ubah
persamaan x2 – 11y2 + 23 = 10xy menjadi
(x
+ y)(x – y) – 10y(x + y) = – 23
(x
+ y)(x – 11y) = – 23
Kasus
1 : (x + y) = 1 dan (x – 11y) = – 23
Solusi
kasus 1 : (– 1, 2)
Kasus
2 : (x + y) = – 1 dan (x – 11y) = 23
Solusi
kasus 2 : (1, – 2)
Kasus
3 : (x + y) = 23 dan (x – 11y) = – 1
Solusi
kasus 3 : (21, 2)
Kasus
4 : (x + y) = – 23 dan (x – 11y) = 1
Solusi
kasus 4 : (– 21, – 2)
│x1│
+ │x2│ + │x3│ + │x4│ = │– 1│ + │1│ + │21│ + │–
21│
=
1 + 1 + 21 + 21
=
44
Subscribe to:
Post Comments (Atom)
Posts
