যদি \(\rm 7a - {7\over a} + 4 = 0\) হয়, তাহলে \(\rm a^3 - {1 \over a^3} - 1\) এর মান নির্ণয় করো।

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 2)
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  1. \(-995 \over 343\)
  2. \(-875 \over 248\)
  3. \(-694 \over 315\)
  4. \(-765 \over 262\)

Answer (Detailed Solution Below)

Option 1 : \(-995 \over 343\)
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Detailed Solution

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প্রদত্ত:

7a - (7/a) = - 4

ব্যবহৃত সূত্র:

যদি a + (1/a) = P হয়

⇒ a3 - (1/a3) = P3 + 3P

গণনা:

7a - (7/a) = - 4

⇒ a - (1/a) = (- 4/7)

⇒ a3 - (1/a3) = (- 4/7)3 + 3 x (- 4/7)

⇒ (- 64/343) - 12/7

⇒ (- 64 - 588)/343

⇒ a3 - (1/a3) = (- 652/343)

a3 - (1/a3) - 1

- 652/343 - 1

⇒ (- 652 - 343)/343

⇒ - 995/343

∴ সঠিক উত্তর হল (- 995/343)

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