Question

if x is equal to 2 + root 3 find the value of x cube minus one upon x cube​

Answer 1

x =2+√3

1/x = 1/(2+√3) = (2-√3)/(2+√3)(2-√3) = (2-√3)/(4-3) = (2-√3)

x -1/x => (2+√3)-(2-√3) => 2√3

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

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

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

${x}^{3} - \frac{1}{ {x}^{3}} = 2 \sqrt{3}(12 + 3) = 2 \sqrt{3}(15)$

$= > {x}^3 - \frac{1}{ {x}^{3}} = 30 \sqrt{3}$

Hope it helps you.