Question

A+1/A=8
THEN
A-1/A=?

Answer 1

squaring in both side
${(A+ \frac{1}{A})}^{2} = {8}^{2}$
${A}^{2} + \frac{1}{ {A \: }^{2} } + 2 = 64$
subtracting both side by 4
${A}^{2} + \frac{1}{ {A \: }^{2} } \: + 2 - 4 = 64 - 4$
${A}^{2} + \frac{1}{ {A \: }^{2} } \: - 2 = 60$
${(A - \frac{1}{A})}^{2} = ( {2 \sqrt{15}) }^{2}$
so
${(A - \frac{1}{A})} = 2 \sqrt{15}$
hope it helps you