Question

Cho biểu thức:

     \(\dfrac{5\sqrt{x}-2}{\sqrt{x}+1}\)

a) Tính P khi \(x=4+2\sqrt{3}\)

b) Tìm P_Min

 

Answer 1

\(\sqrt{x}=\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

\(\Rightarrow P=\dfrac{5\left(\sqrt{3}+1\right)-2}{\sqrt{3}+1+1}=-9+7\sqrt{3}\)

\(P+2=\dfrac{5\sqrt{x}-2}{\sqrt{x}+1}+2=\dfrac{7\sqrt{x}}{\sqrt{x}+1}\ge0\Rightarrow P\ge-2\)

\(P_{min}=-2\) khi \(x=0\)