If x4 + x-4 = 194, x > 0
Find (x - 2)2.
Answer & explanation
Correct answer: option 4
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