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InterviewSolution
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If \(a-\dfrac{1}{a}=7\), then \(a^3 - \dfrac{1}{a^3}= \ ?\) 1. 3222. 3643. 3574. 343 |
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Answer» Correct Answer - Option 2 : 364 Given: \(a-\dfrac{1}{a}=7\) Formula used: (a – b)3 = a3 – b3 – 3ab(a – b) Calculation: \(a-\dfrac{1}{a}=7\) ----1 ⇒ \({\left( {a - \;\frac{1}{a}} \right)^3} = {a^3} - \;\frac{1}{{{a^{3\;}}}}\; - \;\frac{{3a}}{a}\left( {a - \;\frac{1}{a}} \right)\) ⇒ \({a^3} - \;\frac{1}{{{a^{3\;}}}}\; = \;{\left( {a - \;\frac{1}{a}} \right)^3} + 3\left( {a - \;\frac{1}{a}} \right)\;\) ⇒ a3 – 1/a3 = 73 + 3 × 7 ⇒ 343 + 21 ⇒ 364 ∴ \({a^3} - \;\frac{1}{{{a^{3\;}}}}\; = 364\;\) |
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