if a4+1/a4=23,find a3+1/a3
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Step-by-step explanation:
a⁴ + 1/a⁴ = 23
a⁴ + 1/a⁴ + 2 = 25
(a² + 1/a²)² = 25
a² + 1/a² = √25 = 5
a² + 1/a² + 2 = 7
(a + 1/a)² = 7
a + 1/a = √7
(a + 1/a)³ = (√7)³
a³ + 1/a³ + 3(a + 1/a) = 7√7
a³ + 1/a³ = 7√7 - 3√7
= 4√7
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