Question

Evaluate x^4+1÷x^4 if x-1÷x=6

Answer 1

$x - \frac{1}{x} = 6$
$x^{2} + \frac{1}{x^{2}} - 2 = 6*6 = 36$        [Squaring both sides with $(a+b)^{2}$ formula]
$x^{2} + \frac{1}{x^{2}} = 36 + 2 = 38$        [Transposition]
$x^{4} + \frac{1}{x^{4}} + 2 = 38*38 = 1444$         [Squaring again]
$x^{4} + \frac{1}{x^{4}} = 1444 - 2 = 1442$        [Transposition]

Therefore, answer is 1442.