Given $$ a^{1/2}+a^{-1/2}=3 $$ ,find the value of $$ \dfrac{a^2+a^{-2}+1}{a+a^{-1}-1} $$

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Uniteasy Admin · Accepted Answer

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

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