Question

if x/2=1/2x+1 then (x³-1/x³) =?​

Answer 1

${x}^{3} - \frac{1}{ {x}^{3} } = 14$

Step-by-step explanation:

Given :

$\frac{x}{2} = \frac{1}{2x} + 1$

To find :

${x}^{3} - \frac{1}{ {x}^{3} }$

Solution :

$\frac{x}{2} = \frac{1}{2x} + 1 \\ => \frac{x}{2} - \frac{1}{2x} = 1 \\ => \frac{ {x}^{2} - 1}{2x} = 1 \\ => \frac{ {x}^{2} - 1}{x} = 2 \\ => x - \frac{1}{x} = 2$

Now, cubing throughout, we get,

${(x - \frac{1}{x} )}^{3} = 8 \\ => \: {x}^{3} - \frac{1}{ {x}^{3} } - 3(x - \frac{1}{x} ) = 8 \\ => {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 2 = 8 \\ => {x}^{3} - \frac{1}{ {x}^{3} } = 8 + 6 = 14$

Hence, the answer is 14.