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Multiple Choice Questions

If x 1 x 1 than x50 x51 x52 x53 x54 x55 ........

Mathematics (NDA) Algebra

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If x + 1/x = 1 than x⁵⁰ + x⁵¹ + x⁵² + x⁵³ + x⁵⁴ + x⁵⁵ = ?

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Explanation:

x + 1/x = 1
x² – x + 1 = 0
x³ + 1 = 0
x³ = – 1
x⁵⁰ + x⁵¹ + x⁵² + x⁵³ + x⁵⁴ + x⁵⁵
= x⁵⁰ + x⁵¹ + x⁵² + x⁵³ + x⁵⁴ + x⁵⁵
= x⁵⁰ + x³ . x⁵⁰ + x⁵¹ + x³ . x⁵¹ + x⁵² + x³. x⁵²
= x⁵⁰ – x⁵⁰ + x⁵¹ – x⁵¹ + x⁵² – x⁵²
= 0