Question

Answer 1

b) \(B=\dfrac{x+\sqrt{x}+3\sqrt{x}-3+4-6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)

c) \(S=A.B=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}.\dfrac{\sqrt{x}+1}{\sqrt{x}+5}=\dfrac{\sqrt{x}-1}{\sqrt{x}+5}=1-\dfrac{6}{\sqrt{x}+5}\ge1-\dfrac{6}{0+5}=-\dfrac{1}{5}\)

\(minS=-\dfrac{1}{5}\Leftrightarrow x=0\)