If a⁴+1/a⁴=119,then find the value of a3-1/a³
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Step-by-step explanation:
(a² + 1/a²)² = a⁴+1/a⁴ + 2(a²)(1/a²)
but given, a⁴+1/a⁴ = 119
=> (a² + 1/a²)² = 119 + 2 = 121
=> a² + 1/a² = √121 = 11
=> a² + 1/a² = 11 --------------- (1)
(a - 1/a)² = a² + 1/a² - 2(a)(1/a)
=> (a - 1/a)² = 11 - 2 = 9
=> a - 1/a = √9 = 3
=> a - 1/a = 3 ----------------- (2)
a³-1/a³ = (a - 1/a) [ a² + 1/a² + (a) (1/a) ]
=> a³-1/a³ = 3 ( 11 + 1 ) = 3 x 12
.•. a³-1/a³ = 36
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