If b - 1/b = 3 then calculate the value of b⁶ + 1/b⁶?
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Correct answer: A
Explanation
Given:
b - 1/b = 3
By the formula:
(b - 1/b)² = b² + 1/b² - 2
b - 1/b = 3
(b - 1/b)² = 9
b² + 1/b² - 2 = 9
b² + 1/b² = 11
(b² + 1/b²)² = b⁴ + 1/b⁴ + 2
11² = b⁴ + 1/b⁴ + 2
12² = b⁴ + 1/b⁴ + 2
b⁴ + 1/b⁴ = 119
(b² + 1/b²)(b⁴ + 1/b⁴) = b⁶ + 1/b⁶ + b² + 1/b²
11 × 119 = b⁶ + 1/b⁶ + 11
1309 = b⁶ + 1/b⁶ + 11
b⁶ + 1/b⁶ = 1298