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find the value of x :

4[x² + 1/x²] - [x + 1/x] = 60

4 (x^{2} + \frac{1}{x^{2}}) - (x + \frac{1}{x}) = 60 4 ({(x + \frac{1}{x})}^{2} - 2) - (x + \frac{1}{x}) = 60 (b e c a u s e a^{2} + b^{2} = (a + b)^{2} - 2 a b) 4 {(x + \frac{1}{x})}^{2} - 8 - (x + \frac{1}{x}) = 60 4 {(x + \frac{1}{x})}^{2} - (x + \frac{1}{x}) - 68 = 0 P u t x + \frac{1}{x} = t 4 t^{2} - t - 68 = 0 4 t^{2} + 16 t - 17 t - 68 = 0 4 t (t + 4) - 17 (t + 4) = 0 (t + 4) (4 t - 17) = 0 t = - 4 o r t = \frac{17}{4} x + \frac{1}{x} = - 4 o r x + \frac{1}{x} = \frac{17}{4} x^{2} + 4 x + 1 = 0 o r 4 x^{2} - 17 x + 4 = 0 x = \frac{- 4 \pm \sqrt{15}}{2} o r x = 4 o r x = 0.25

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