2018 · Q25
If ab + bc + ca = 0, then the value of (b²-ca)(c²-ab)+(a²-bc)(c²-ab)+(a²-bc)(b²-ca)/(a²-bc)(b²-ca)(c²-ab) is
Elementary MathematicsAlgebra
- A- 1
- B0
- C1
- D2
Explanation
From ab + bc + ca = 0, we get a^2 - bc = a(a + b + c), and similarly b^2 - ca = b(a + b + c), c^2 - ab = c(a + b + c). Each term of the numerator then contains the factor (ab + bc + ca), so the numerator is 0 while the denominator is nonzero. The expression equals 0. Hence option B.