If x⁴ + \(\frac{1}{x^4}\) = 49727, the positive value of ( x + \(\frac{1}{x}\) -15 ) is?

0

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 + \(\frac{1}{x^4}\) = 49727

x² + \(\frac{1}{x^2}\) = \(\sqrt {49727 + 2}\) = 223

So, ( x + \(\frac{1}{x}\) - 15 ) = ( \(\sqrt {223 + 2}\) - 15 ) = 0