Question

BÀi 2:

Answer 1

a)

\(P=\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)

\(=\left[\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}+\sqrt{a}\right]\left[\dfrac{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}+a\right)}{1+\sqrt{a}}-\sqrt{a}\right]\)

\(=\left(a+2\sqrt{a}+1\right)\left(a-2\sqrt{a}+1\right)\)

\(=\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)^2\)

\(=\left(a-1\right)^2\)

b)

\(\left(a-1\right)^2< 7-4\sqrt{3}\)

\(\Leftrightarrow\left(a-1\right)^2< \left(2-\sqrt{3}\right)^2\)

\(\Leftrightarrow a-1< 2-\sqrt{3}\)

\(\Leftrightarrow a< 3-\sqrt{3}\)