Question

if x-1/x=3+2root2,find the value of x^3-1/x^3

Answer 1

...........................................may help u

Answer 2

Answer:

The value of $\bold{x^{3}-\frac{1}{x}^{3}=215.47}$

Step-by-step explanation:

To find: Value of $x^{3}-\frac{1}{x^{3}}$

According to formulae,

$\begin{array}{l}\bold{{(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)}} \\ {a=x \text { and } b=\frac{1}{x}} \\ {\left(x-\frac{1}{x}\right)^{3}=x^{3}-\frac{1}{x}^{3}-3 . x \cdot \frac{1}{x}\left(x-\frac{1}{x}\right)}\end{array}$

As the question says  

$x-\frac{1}{x}=3+2 \sqrt{2}$

Now applying the formula, we get,

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

Solving the equation,

$\begin{array}{l}{(3+2 \sqrt{2})^{3}+3(3+2 \sqrt{2})=x^{3}-\frac{1^{3}}{x}} \\ {195.112+17.48=x^{3}-\frac{1^{3}}{x}} \\ {215.47=\mathrm{x}^{3}-\frac{1^{3}}{\mathrm{x}}}\end{array}$

Thus the value of $x^{3}-\frac{1}{x}^{3}=\bold{215.47}$