Question

help me ye bahut important he ​

Answer 1

Answer:

$\boxed{ \boxed {\bold{ \huge{ \pink{ 14}}}}}$

Step-by-step explanation:

$\dfrac{ {x}^{2} - 1 }{x} = 2 \\ \dfrac{ {x}^{2} }{x} - \dfrac{1}{x} = 2 \\ x - \dfrac{1}{x} = 2 \\ squaring \: both \: sides \\ {(x - \dfrac{1}{x} )}^{2} = {2}^{2} \\ {x}^{2} + \dfrac{1 }{ {x}^{2} } - 2 \: x \: \dfrac{1}{x} = 4 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 = 4 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } = 4 + 2 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } = 6$

$\dfrac{ {x}^{6} - 1}{ {x}^{3} } \\ = \dfrac{ {x}^{6} }{ {x}^{3} } - \dfrac{1}{ {x}^{3} } \\ = {x}^{3} - \dfrac{1}{ {x}^{3} } \\ = {(x)}^{3} - { (\dfrac{1}{x} )}^{3} \\ = (x - \dfrac{1}{x} ) \: ( {x}^{2} + \dfrac{1}{ {x}^{2} } + x \: \dfrac{1}{x} )$

$= (2) \: (6 + 1)$

$= 2 \: \times 7 \\ = 14$