Question

given that a^1/2 - a^-1/2=1,prove that a + a^-1=3

Answer 1

a-2+a^-1=1

Answer 2

thus, a+a^-1=3

Answer 3

am i rite

Answer 4

I think so

Answer 5

\[\sqrt a-\frac{1}{\sqrt a}=1~~\iff~~a-1=\sqrt a~~\iff~~a^2-3a+1=0\]
Finding the roots, you should have
\[a=\frac{3\pm\sqrt{5}}{2}\]
Show that
\[a+\frac{1}{a}=\frac{3\pm\sqrt{5}}{2}+\frac{2}{3\pm\sqrt5}=3\]