Question

Answer 1

`a)`\(P=\left(\dfrac{4a}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{a}}\right).\dfrac{\sqrt{a}-1}{a^2}\)

\(P=\left(\dfrac{4a\sqrt{a}-\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right).\dfrac{\sqrt{a}-1}{a^2}\)

\(P=\dfrac{4a-1}{\sqrt{a}-1}.\dfrac{\sqrt{a}-1}{a^2}\)

\(P=\dfrac{4a-1}{a^2}\)

`b)`\(P=3\)

\(\Leftrightarrow\dfrac{4a-1}{a^2}=3\)

\(\Leftrightarrow3a^2=4a-1\)

\(\Leftrightarrow3a^2-4a+1=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=1\left(ktm\right)\\a=\dfrac{1}{3}\left(tm\right)\end{matrix}\right.\)