Question

rút gọn và tìm gtln của nó

Answer 1

ĐKXĐ: x>=0

\(A=\dfrac{\sqrt{x}\left(x\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{x-3}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}+1}-\dfrac{x-3}{\sqrt{x}+1}\)

\(=\dfrac{x-\sqrt{x}-x+3}{\sqrt{x}+1}=\dfrac{-\sqrt{x}+3}{\sqrt{x}+1}\)

\(=\dfrac{-\sqrt{x}-1+4}{\sqrt{x}+1}=-1+\dfrac{4}{\sqrt{x}+1}\)

\(\dfrac{4}{\sqrt{x}+1}< =\dfrac{4}{1}=4\)

=>\(\dfrac{4}{\sqrt{x}+1}-1< =4-1=3\)

Dấu = xảy ra khi x=0