Question

x³+1/x³ =110 , find x+1/x​

Answer 1

Answer:

$\huge x + \frac{1}{x} = 5$

Step-by-step explanation:

${x}^{3} + \frac{1}{ {x}^{3} } = 110 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 110 \\ {(x + \frac{1}{x} )}^{3} - 3(x + \frac{1}{x} ) = 110 \\ Let \: \: \: { \large x + \frac{1}{x} } \: \: \: be \: \: {\large k} \\ {k}^{3} - 3k = 110 \\ k( {k}^{2} - 3) = 110 \\ k( {k}^{2} - 3) = 5( {5}^{2} - 3) \\ \boxed{ \large k = \underline{ \underline{ \bf 5}}}$