Question
Download Solution PDFयदि \({\rm x} + \frac{1}{{\rm x}} = - 14 \) है और x < -1 है, तो \({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}} \) का मान क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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) × (\(-8\sqrt 3 \))
⇒ \(112\sqrt 3 \)
Last updated on Jul 10, 2025
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