ada dua buah bilangan, dimisalkan a dan b. jika dikalikan menghasilkan n, jika dijumlahkanjuga menghasilkan n, jika dibagi juga menghasilkan nilai n. berapakah a, b, dan n?
a=1/2
b=-1
n=-1/2
Alasan:
dari soal di atas, dapat kita buat persamaan-persamaan berikut:
a+b=n
a.b=n
a/b=n
n = a + b
...
ab = a + b
ab – b = a
b(a – 1) = a
b = a/(a – 1)
a/(a/(a – 1)) = a + a/(a – 1)
a – 1 = a + a/(a – 1)
(a – 1)² = a(a – 1) + a
a² – 2a + 1 = a² – a + a
–2a + 1 = 0
–2a = –1
a = 1/2
b = (1/2)/(1/2 – 1)
b = (1/2)/(–1/2)
b = –1
n = 1/2 – 1
n = –1/2
cek:
1/2 + (–1) = –1/2
(1/2)(–1) = –1/2
(1/2)/(–1) = –1/2
Sehingga, a = 1/2 and b = –1.
Sumber : http://www.facebook.com/TeachersofMathematics