\(7 b-\frac{1}{4 b}=7\) , అయిన \(16 b^2+\frac{1}{49 b^2}\) విలువ ఎంత?

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)
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  1. \( \frac{80}{49} \)
  2. \( \frac{104}{7} \)
  3. \(\frac{120}{7} \)
  4. \( \frac{7}{2}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{120}{7} \)
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Detailed Solution

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సూత్రం ఉపయోగించబడింది

(a - b) 2 = a 2 + b 2 - 2ab

లెక్కింపు

సమీకరణంను 4/7తో గుణించడం.

4/7 × (7b - 1/4b) = 7 × 4/7

4b - 1/7b = 4

రెండు వైపులా వర్గం చేయడం:

⇒ (4b - 1/7b)2 = 42

⇒ \(16 b^2+\frac{1}{49 b^2}\)- 2 × 4 × 1/7 = 16

⇒ \(16 b^2+\frac{1}{49 b^2}\) = 16 + 8/7

⇒ \(16 b^2+\frac{1}{49 b^2}\) = 120/7

విలువ 120/7.

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