If x4 + x-4 = 194, x > 0 Find (x - 2)2.

1 2 -3 3

3

Formula → x4 + \(\frac{1}{x^4}\) = a             →  x2 + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\)   x4 + \(\frac{1}{x^4}\) = 194 x2 + \(\frac{1}{x^2}\) = \(\sqrt {194 + 2}\) = 14 x + \(\frac{1}{x}\) = \(\sqrt {14 + 2}\) = 4 x2 + 1 = 4x x2 - 4x = -1 Now, we have to find (x - 2)2   x2 - 4x + 4 = -1 + 4 = 3