If a - 1/a = 2 then calculate the value of a⁴ + 1/a4?
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Correct answer: B
Explanation
Given:
a − 1/a = 2
By the formula:
(a − 1/a)² = a² + 1/a² − 2
(a − 1/a)² = 2²
4 = a² + 1/a² − 2
a² + 1/a² = 6
(a²+ 1/a²)² = a⁴ + 1/a⁴ + 2
6² = a⁴ + 1/a⁴ + 2
36 = a⁴ + 1/a⁴ + 2
a⁴ + 1/a⁴ = 34