Question

if x=3 -2 root 2 , find x cube - 1/x cube



plz help...​

Answer 1

Answer:

$-128\sqrt{2}$

Step-by-step explanation:

We can see that the -1/x^3 needs to be rationalized because of root.

Rationalizing the Denominator, we get:

$\frac{1}{3-2\sqrt{2} }$ × $\frac{3+2\sqrt{2} }{3+2\sqrt{2} }$

$=3 + 2\sqrt{2}$.     Denominator gets canceled by applying the formula $a^{2} - b^{2}$

Now we take the rationalized equation to our question.

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

3 gets cancelled of and we get:

$(-2\sqrt{2} - 2\sqrt{2}) ^{3} = (-4\sqrt{2})^{3} \\= -128\sqrt{2}$