Question

if x + 1/x = 5 . Find x³ + 1/x³​

Answer 1

Answer:

$x + \frac{1}{x} = 5 \\ \\ x + 1 = 5x \\ \\ 1 = 5x - x \\ \\ 1 = 4x \\ \\ \frac{1}{4} = x \\ \\ \\ = {x}^{3} + \frac{1}{ {x}^{3} } \\ \\ = ( \frac{1}{4} ) ^{3} + \frac{1}{ (\frac{1}{4}) ^{3} } \\ \\ = \frac{1}{64} + \frac{1}{ \frac{1}{64} } \\ \\ = \frac{1}{64} + \frac{64}{1} \\ \\ = \frac{1 \times 1 + 64 \times 64}{64 \times 1} \\ \\ = \frac{1 + 4096}{64} \\ \\ = \frac{4097}{64}$