यदि  \({\rm x} + \frac{1}{{\rm x}} = - 14 \)  है और x < -1 है, तो \({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}} \) का मान क्या होगा? 

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)
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  1. - 112√3  
  2. 112√3  
  3. -140√2  
  4. 140√2  

Answer (Detailed Solution Below)

Option 2 : 112√3  
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Detailed Solution

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दिया गया है:

\({\rm x} + \frac{1}{{\rm x}} = - 14\)

प्रयुक्त अवधारणा:

(a2 - b2) = (a + b)(a - b)

गणना:

∴ अभीष्ट उत्तर  \(112\sqrt 3 \) है।

\({\rm x} + \frac{1}{{\rm x}} = - 14 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2= 196 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2-4= 196-4 \)

⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} -2= 192 \)

⇒ \(({\rm x} - \frac{1}{{\rm x}})^2= 192 \)

⇒ \({\rm x} - \frac{1}{{\rm x}} =\pm 8√3 \)

चूँकि x < -1 है इसलिए, \({\rm x} - \frac{1}{{\rm x}} =- 8\sqrt3\)

अब,

\({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}\) = (- 14) ×  (\(-8\sqrt 3 \))

⇒ \(112\sqrt 3 \)

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