If \(x + \left( {\frac{1}{x}} \right) = 12\) and \({x^2} - \frac{1}{{{x^2}}} = 50\), then the value of \({x^4} - \frac{1}{{{x^4}}} \) is:

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Answer: (D) 7100

Explanation

x⁴ − 1/x⁴ = (x² − 1/x²)(x² + 1/x²). With x + 1/x = 12, x² + 1/x² = 144 − 2 = 142. Using the given x² − 1/x² = 50, the value = 50 × 142 = 7100.