Question

2. If X + (1/X) = 2, then (X) cube + (1/X cube) = ?

a) 2
b) 8
c) 14
d) 64​

Answer 1

Step-by-step explanation:

$x + \frac{1}{x} = 2 \\ therefore \\ {(x \ + \frac{1}{x} )}^{2} = {x}^{2} + { \frac{1}{ {x}^{2} } } + 2 \\ {2}^{2} = {x}^{2} + { \frac{1}{ {x}^{2} } } + 2 \\ {x}^{2} + { \frac{1}{ {x}^{2} } } = 4 - 2 \\ {x}^{2} + { \frac{1}{ {x}^{2} } } = 2$WE KNOW THAT

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

SO,

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

THEREFORE APPLYING ALL THE VALUES WE WOULD GET

${x}^{3} + { \frac{1}{ {x}^{3} } } = (2)(2 - 1) \\ {x}^{3} + { \frac{1}{ {x}^{3} } } = 2(1) \\ {x}^{3} + { \frac{1}{ {x}^{3} } } = 2$