Question

[HMinhTD]

MN GIÚP MÌNH BÀI NÀY ĐƯỢC KHÔNG Ạ

Answer 1

[tuan manh]

a, đkxđ: \(x\ge0\)
\(A=\dfrac{\sqrt{x}}{\sqrt{x}+3}=\dfrac{1}{4}\Leftrightarrow\sqrt{x}+3=4\sqrt{x}\Leftrightarrow3=3\sqrt{x}\Leftrightarrow\sqrt{x}=1\Leftrightarrow\left(\sqrt{x}\right)^2=1^2\Leftrightarrow x=1\)
b,
\(B=\dfrac{2\sqrt{x}-2}{x-2\sqrt{x}+1}+\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{2\sqrt{x}-2}{\left(\sqrt{x}-1\right)^2}+\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)^2}=\dfrac{2\sqrt{x}-2+x-1}{\left(\sqrt{x}-1\right)^2}=\dfrac{\left(\sqrt{x}+1\right)^2-4}{\left(\sqrt{x}-1\right)^2}=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-1\right)^2}=\dfrac{\sqrt{x}+3}{\sqrt{x}-1}\)
c,
\(A.B< 0\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}+3}.\dfrac{\sqrt{x}+3}{\sqrt{x}-1}< 0\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}-1}< 0\)
do \(\sqrt{x}\ge0\) mà \(\frac{\sqrt{x}}{\sqrt{x}-1}<0\Leftrightarrow \sqrt{x}-1<0\Leftrightarrow \sqrt{x}<1\Leftrightarrow x<1\)