Question

If x-1/x=root under5.then find x cube +1/xcube​

Answer 1

put the both value of x in equatiin one by one by making two casses

Answer 2

${(x + \frac{1}{x}) }^{2} = {(x - \frac{1}{x} ) }^{2} + 4(x)( \frac{1}{x} ) \\ ( {x + \frac{1}{x}) }^{2} = ( { \sqrt{5}) }^{2} + 4 = 5 + 4 = 9 \\ x + \frac{1}{x} = 3 \: or \: - 3 \\ ( {x + \frac{1}{x}) }^{3} = {x}^{3} + { (\frac{1}{x}) }^{3} + 3(x + \frac{1}{x} ) \\ \\ if \: x \: = 3 \\ {x}^{3} + { (\frac{1}{x}) }^{3} = {3}^{3 -} - (3 \times 3) = 27 - 9 = 18 \\ \\ if \: x \: = - 3 \\ {x}^{3} + \frac{1}{ {x}^{3} } = {( - 3)}^{3} - (3 \times ( - 3)) = - 27 + 9 = - 18$