समजा, \(\rm x+\frac{1}{x}=-6\) तर \(\rm x^5+\frac{1}{x^5}\) चे मूल्य किती?

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Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 3)

Answer 1

दिलेल्याप्रमाणे :

x + (1/x) = - 6

वापरलेले सूत्र :

समजा x + (1/x) = P, तर

⇒ x2 + (1/x2) = (P2 - 2)

समजा x + (1/x) = P, तर

⇒ x3 + (1/x3) = P3 - 3P

x5 + (1/x5) = {x3 + (1/x3)} × {x2 + 1/x2} - {x + (1/x)}

गणना :

x + (1/x) = - 6

⇒ x2 + (1/x2) = (- 6)2 - 2

⇒ 36 - 2 = 34

आता,

x + (1/x) = - 6

⇒ x3 + (1/x3) = (- 6)3 - 3 (- 6)

⇒ (- 216) + 18 = (- 198)

x5 - (1/x5) = {x3 + (1/x3)} × {x2 + 1/x2} - {x + (1/x)}

⇒ (- 198) × 34 - (- 6)

⇒ (- 6732) + 6 = - 6726

∴ योग्य उत्तर - 6726 हे आहे.