Maths · Binomial theorem for a positive integral index
If and find:
If \( a \neq 0 \) and \( a-\frac{1}{a}=4, \) find: \( a^{3}-\frac{1}{a^{3}} \)
- A. 76
- B. 71
- C. 45
- D. 16
Step-by-step solution
Using the identity (a - 1/a)^3 = a^3 - 1/a^3 - 3(a - 1/a), we have a^3 - 1/a^3 = (a - 1/a)^3 + 3(a - 1/a) = 4^3 + 3*4 = 64 + 12 = 76.
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