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InterviewSolution
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IF x = 3 + √8, find the value of \({x^3} + \frac{1}{{{x^3}}}\).1. 2162. 1983. 2004. 196 |
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Answer» Correct Answer - Option 2 : 198 Given: x = 3 + √8 Calculation: as x = 3 + √8 (1/x) = 1/(3 + √8) Rationalising we get, (1/x) = 3 - √8 Then, x + (1/x) = 3 + √8 + 3 - √8 = 6 ----(1) taking cube of (1) we get, [x + (1/x)]3 = 63 x3 + (1/x)3 + 3 × x × (1/x) [x + (1/x)] = 216 x3 + (1/x)3 + 3 × [x + (1/x)] = 216 x3 + (1/x)3 = 216 - 3 × [x + (1/x)] x3 + (1/x)3 = 216 - 3 × 6 = 198 ∴ The value of x3 + (1/x)3 is 198. |
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