Question

If x=2-✓3, find the value of x-1/x3

Answer 1

Answer:

-19-11$\sqrt{3}$

Step-by-step explanation:

$\frac{2-\sqrt{3} -1}{(2-\sqrt{3})^{3} }$  subtract 2-1 in the numerator, and expand (a-b)^3 in the denominator=$\frac{1-\sqrt{3} }{2-12\sqrt{3} +18-3\sqrt{3} }$,add the numbers and collect like terms in the denominator=

$\frac{1-\sqrt{3} }{26-15\sqrt{3} }$, multiply the fraction by$\frac{26-15\sqrt{3} }{26-15\sqrt{3} }$=

$\frac{(1-\sqrt{3})(26+15\sqrt{3 } }{(26-15\sqrt{3})(26+15\sqrt{3} ) }$, using (a+b)(a-b)=a^2-b^2 simplify the product, multiply the numbers in the denominator,you should get 1 and because any number divided by 1 remains the same, we get$(1-\sqrt{3} )(26+15\sqrt{3} )$, we simplify the expression and we get -19-11$\sqrt{3}$.