Question

M=A.B 

A=\(\dfrac{x}{\sqrt{x}-2}\),B=\(\dfrac{\sqrt{x}-2}{\sqrt{x}+2}\)

Tìm GTNN của M

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >4\end{matrix}\right.\)

\(M=A\cdot B=\dfrac{x}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}-2}{\sqrt{x}+2}\)

=>\(M=\dfrac{x}{\sqrt{x}+2}\)

=>\(M=\dfrac{x-4+4}{\sqrt{x}+2}=\sqrt{x}-2+\dfrac{4}{\sqrt{x}+2}\)

=>\(M=\sqrt{x}+2+\dfrac{4}{\sqrt{x}+2}-4\)

=>\(M>=2\cdot\sqrt{\left(\sqrt{x}+2\right)\cdot\dfrac{4}{\sqrt{x}+2}}-4=0\)

Dấu '=' xảy ra khi \(\sqrt{x}+2=\sqrt{4}=2\)

=>\(\sqrt{x}=0\)

=>x=0(nhận)