COMEDK2018MathematicsBasics of Mathematics
If 3 x²-2 x+4 (x-1)⁶ = A₁ x+1 + A₂ (x+1)² + A₃ (x+1)³ + A₄ (x+1)⁴ + A₅ (x+1)⁵ + A₆ (x+1)⁶ , then (A₁+A₂+A₂-A₄-A₆ )=
Options
- A(0,0)
- B(-8,-12)
- C(8,-12)
- D(-8,12)
Correct answer
D. (-8,12)
Step-by-step solution
We have, aligned 3 x²-2 x+4 (x-1)⁶ = A₁ x+1 &+ A₂ (x+1)² + A₃ (x+1)³ &+ A₄ (x+1)⁴ + A₅ (x+1)⁵ + A₆ (x+1)⁶ ( i ) aligned Now, put x=0 in Eq. (i), we get A₁+A₂+A₃+A₄+A₅+A₆=4 If A₁+A₃+A₅=-8 and A₂+A₁+A₆=12 satisfies the equation. Hence, only option (i.e. -8,12 ) satisfies the solution.