\(ĐKXĐ:x\ge0;x\ne1;0\)
\(A=\frac{2x+2}{\sqrt{x}}+\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(A=\frac{2x+2}{\sqrt{x}}+\frac{x+\sqrt{x}+1}{\sqrt{x}}-\frac{x-\sqrt{x}+1}{\sqrt{x}}\)
\(A=\frac{2x+2+x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}\)
\(A=\frac{2x+2+2\sqrt{x}}{\sqrt{x}}\)
\(A=2\sqrt{x}+\frac{2}{\sqrt{x}}+2\)
a/d bđt cauchy
\(2\sqrt{x}+\frac{2}{\sqrt{x}}\ge2\sqrt{2.2}=2.2=4\)
\(A\ge4+2=6\)
\(< =>A>5\)
dấu "=" xảy ra khi x=1
