Question

If x+1/x = 6 find the values of i) x-1/x ii) xsquare - 1/xsquare
Solve and answer with process please.

Answer 1

$x + \frac{1}{x} = 6$

(i)${(x - \frac{1}{x})}^{2} = {(x + \frac{1}{x} )}^{2} - 4$

${(x - \frac{1}{x})}^{2} = {6}^{2} - 4$

${(x - \frac{1}{x})}^{2} = 36 - 4$

${(x - \frac{1}{x})}^{2} = 32$

$\fbox{(x - \frac{1}{x}) = +/- \sqrt{32} }$

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

$(6)( \sqrt{32} ) = {x}^{2} - \frac{1}{ {x}^{2} }$

$\fbox{{x}^{2} - \frac{1}{ {x}^{2} } = 6 \sqrt{32} }$