Binomial Expansion
The term independent of x in the expansion of (x² - 1/x)⁹ is
Select the correct option:
Solution
84
- General Term: For (x2−x−1)9, the general term is:
- Tr+1=(r9)(x2)9−r(−x−1)r
- Tr+1=(r9)(x)18−2r(−1)r(x)−r=(r9)(−1)rx18−3r
- Independent Condition: For the term to be independent of x, the power of x must be zero:
- 18−3r=0⟹r=6.
- Calculate Value:
- T7=(69)(−1)6x0=(39)⋅1
- T7=3×2×19×8×7=3×4×7=84.
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About This Question
- Subject
- mathematics
- Chapter
- binomial theorem and its simple applications
- Topic
- binomial expansion
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
84
- General Term: For (x2−x−1)9, the general term is:
- Tr+1=(r9)(x2)9−r(−x−1)r
- Tr+1=(r9)(x)18−2r(−1)r(x)−r=(r9)(−1)rx18−3r
- Independent Condition: For the term to be independent of x, the power of x must be zero:
- 18−3r=0⟹r=6.
- Calculate Value:
- T7=(69)(−1)6x0=(39)⋅1
- T7=3×2×19×8×7=3×4×7=84.
This medium difficulty mathematics question is from the chapter binomial theorem and its simple applications, covering the topic of binomial expansion. It appeared in the 2025 exam.
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