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If a + 1/a = -2 then the value of a1000 + a- 1000 is

Question

If a + 1/a = -2 then the value of a1000 +

a- 1000 is

A 2 Correct Answer Incorrect Answer

C 1 Correct Answer Incorrect Answer

D 1/2 Correct Answer Incorrect Answer

Solution

a + 1/a = –2 let a = -1 -1 + = 1/-1+-1 = -2 ∴ a = −1 a ¹⁰⁰⁰ + a⁻¹⁰⁰⁰ = (−1) ¹⁰⁰⁰ + (−1)⁻¹⁰⁰⁰ = 1 + 1 = 2

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