Question
Given a^{1/2}+a^{-1/2}=3 ,find the value of \dfrac{a^2+a^{-2}+1}{a+a^{-1}-1}
Given a^{1/2}+a^{-1/2}=3 ,find the value of \dfrac{a^2+a^{-2}+1}{a+a^{-1}-1}
a^{1/2}+a^{-1/2}=3
Square the both sides,
a+a^{-1}+2=9
Square both sides of above equation,
Plug in (1) and (2), we get
\dfrac{a^2+a^{-2}+1}{a+a^{-1}-1}=\dfrac{47+1}{7-1} =8