Question
Download Solution PDFIf \({\rm x} + \frac{1}{{\rm x}} = - 14 \), and x < -1, what will be the value of \({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}\) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\({\rm x} + \frac{1}{{\rm x}} = - 14\)
Concept used:
(a2 - b2) = (a + b)(a - b)
Calculation:
\({\rm x} + \frac{1}{{\rm x}} = - 14 \)
⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2= 196 \)
⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} +2-4= 196-4 \)
⇒ \({\rm x^2} + \frac{1}{{\rm x^2}} -2= 192 \)
⇒ \(({\rm x} - \frac{1}{{\rm x}})^2= 192 \)
⇒ \({\rm x} - \frac{1}{{\rm x}} =\pm 8√3 \)
As x < -1 So, \({\rm x} - \frac{1}{{\rm x}} =- 8\sqrt3 \)
Now,
\({{\rm x}^2} - \frac{1}{{{{\rm x}^2}}}\) = (- 14) × (\(-8\sqrt 3 \))
⇒ \(112\sqrt 3 \)
∴ The required answer is \(112\sqrt 3 \).
Last updated on Jul 9, 2025
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