If x⁴ + \(\frac{1}{x^4}\) = 27887, the positive value of ( x + \(\frac{1}{x}\) -26 ) is:

-13

If x⁴ + \(\frac{1}{x^4}\) = a

then x² + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\) = b

and x + \(\frac{1}{x}\) = \(\sqrt {b + 2}\)

ATQ,

x⁴ + \(\frac{1}{x^4}\) = 27887

x² + \(\frac{1}{x^2}\) = \(\sqrt {27887 + 2}\) = 167

So, ( x + \(\frac{1}{x}\) - 26 ) = ( \(\sqrt {167 + 2}\) - 26 ) = -13