Question

If a+1/a=3, find the value of a5+1/a5​

Answer 1

Solution :-

→ a + 1/a = 3

squaring both sides ,

→ (a + 1/a)² = 3²

→ a² + 1/a² + 2 * a * 1/a = 9

→ (a² + 1/a)² = 9 - 2 = 7

again,

→ a + 1/a = 3

cubing both sides ,

→ (a + 1/a)³ = 3³

→ a³ + 1/a³ + 3 * a * 1/a * (a + 1/a) = 27

→ (a³ + 1/a³) + 3 * 3 = 27

→ (a³ + 1/a³) = 27 - 9 = 18 .

then,

→ (a⁵ + 1/a⁵) = (a² + 1/a)² * (a³ + 1/a³) - (a + 1/a)

putting all values we get,

→ (a⁵ + 1/a⁵) = 7 * 18 - 3

→ (a⁵ + 1/a⁵) = 126 - 3

→ (a⁵ + 1/a⁵) = 123 (Ans.)

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