Question
If x is a complex root of the equation | array ccc 1 & x & x \\ x & 1 & x \\ x & x & 1 array |+ | array ccc 1-x & 1 & 1 \\ 1 & 1-x & 1 \\ 1 & 1 & 1-x array |=0, then x^ 2007 +x^ -2007 =
BITSAT
Mathematics
Determinants
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 1
- B. -1
- C. -2
- D. 2
Answer
C. -2
Step-by-step solution
Expanding the two determinants, we get (1-3 x^2+2 x^3 )+ (3 x^2-x^3 )=0 x^3+1=0 x=- ,- ^2,-1 x^ 2007 +x^ -2007 =-1-1=-2
Related: Mathematics — Determinants · All PYQ Banks