Question

if x-1/x=3/2 find (i) x²-1/x² (ii) x⁴-1/x⁴​

Answer 1

Answer:

$\frac{x - 1}{x} = \frac{3}{2} \\ 3x = 2x - 1 \\ 3x - 2x = - 1 \\ x = - 1$

so x² - 1 / x² =

${x}^{2} - \frac{1}{ {x}^{2} } \\ = {1}^{2} - \frac{1}{ {1}^{2} } \\ \frac{ - 1 - 1}{ - 1} = \frac{ - 2}{ - 1} = 2$

and x⁴ - 1 / x⁴

${x}^{4} - \frac{1}{ {x}^{4} } \\ - {1}^{4} - \frac{1}{ - {1}^{4} } \\ \frac{ - 1 - 1}{ - 1} = \frac{ - 2}{ - 1} = 2$