Question

if X equal to minus root 3 find the value of x minus 1 by 3 holes cube

Answer 1

Hi...☺

Here is your answer...✌

GIVEN THAT,

x = 2 - √3

And

$\frac{1}{x} = \frac{1}{2 - \sqrt{3} } \\ \\ on \: rationalising \: the \: denominator \\we \: get \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{ 3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 + \sqrt{3}$

Now,

${(x - \frac{1}{x} )}^{3} \\ \\ = ( \: 2 - \sqrt{3} -{ ( 2 + \sqrt{3} ) \: )}^{3} \\ \\ = {(2 - \sqrt{3} - 2 - \sqrt{3} )}^{3} \\ \\ ={ ( - 2 \sqrt{3} ) }^{3} \\ \\ = ( - 2 \sqrt{3} ) \times ( - 2 \sqrt{3} ) \times ( - 2 \sqrt{3} ) \\ \\ = - 8 \times 3\sqrt{3} \\ \\ = - 24 \sqrt{3}$