a: \(A=\left(\dfrac{a-1}{2\sqrt{a}}\right)^2\cdot\left(\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{a-1}\right)\)
\(=\dfrac{\left(a-1\right)^2}{a-1}\cdot\dfrac{-4\sqrt{a}}{4a}=\dfrac{-\left(a-1\right)}{\sqrt{a}}\)
b: Để \(A=\dfrac{\sqrt{6}}{\sqrt{6}+1}\) thì \(\dfrac{-\left(a-1\right)}{\sqrt{a}}=\dfrac{\sqrt{6}}{\sqrt{6}+1}\)
\(\Leftrightarrow-\left(a-1\right)\left(\sqrt{6}+1\right)=\sqrt{6a}\)
\(\Leftrightarrow-a\sqrt{6}-a+\sqrt{6}+1-\sqrt{6}\sqrt{a}=0\)
hay \(a\simeq0.706\)
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