Question

if x=3+2√2 find x³-1/x³​

Answer 1

Step-by-step explanation:

3+2√2^3-1/3+2√2^3

solve this u will get the answer easily

Answer 2

$The\ \ value\ \ of: x^{3}-\frac{1}{x^{3}} \ = \ (99-70\sqrt2)$

Step-by-step explanation:

Given that:  $x= 3+2\sqrt{2}$

Find:  $x^{3}-\frac{1}{x^{3}}$

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

Formula:  $(x+y)^3=x^3+y^3+3\cdot x \cdot y(x+y)$

$(x+y)^3=x^3+y^3+3 x^2y+3xy^2$

Solve the value of : $x^{3}$

$(3+2\sqrt{2})^3= 3^3+(2\sqrt2)^3+3\cdot 3\cdot2\sqrt{2}( 3+2\sqrt{2})$

$(3+2\sqrt{2})^3=27+16\sqrt2+18\sqrt2( 3+2\sqrt{2})$

$(3+2\sqrt{2})^3=27+16\sqrt2+54\sqrt2+72$

$(3+2\sqrt{2})^3=99+70\sqrt2$

When value of $x^{3}$ is equal to $99+70\sqrt2$  So, $\frac{1}{x^3}$ value is equal to $\frac{1}{99+70\sqrt2}$

$x^{3}-\frac{1}{x^{3}} = 99+70\sqrt2 \ - \ \frac{1}{99+70\sqrt2}$

$x^{3}-\frac{1}{x^{3}} = \frac {(99+70\sqrt2)(99+70\sqrt2)\ -\ 1}{(99+70\sqrt2)}$

$x^{3}-\frac{1}{x^{3}} = \frac{(99+70\sqrt2 )^2\ - \ 1 }{99+70\sqrt2}$

Formula:  $(a-b)^{2}=(a+b)(a-b)$

$x^{3}-\frac{1}{x^{3}} = \frac{(99+70\sqrt2 )^2\ - \ (1)^2 }{99+70\sqrt2}$

$x^{3}-\frac{1}{x^{3}} = \frac {(99+70\sqrt2)(99-70\sqrt2)}{(99+70\sqrt2)}$

$x^{3}-\frac{1}{x^{3}}= (99-70\sqrt2)$

Learn more:

• formula of $(a+b)^3$: https://brainly.in/question/5177811