If $x^4+\frac{1}{x^4}=194$ and $x^3+\frac{1}{x^3}=?$
Answer & explanation
Correct answer: option 1
If x4 + \(\frac{1}{x^4}\) = a
then x2 + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\) = b
and x + \(\frac{1}{x}\) = \(\sqrt {b + 2}\)
$x^4+\frac{1}{x^4}=194$
= x2 + \(\frac{1}{x^2}\) = \(\sqrt {196 + 2}\) = 14
= x + \(\frac{1}{x}\) = \(\sqrt {14 + 2}\) = 4
$x^3+\frac{1}{x^3}$ = 43 - 3 × 4 = 52