Question

if x=√3-√2,find the value of x^3+1/x^3​

Answer 1

Answer:

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