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a: \(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}\)
\(=\sqrt{a}-\sqrt{b}-\sqrt{a}-\sqrt{b}=-2\sqrt{b}\)
b: \(B=\dfrac{2\sqrt{x}-x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{x-1}\)
\(=\dfrac{-2x+\sqrt{x}-1}{\sqrt{x}-1}\cdot\dfrac{1}{x-1}\)
c: \(C=\dfrac{x-9-x+3\sqrt{x}}{x-9}:\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+3}+\dfrac{x-9}{x+\sqrt{x}-6}\right)\)
\(=\dfrac{3\left(\sqrt{x}-3\right)}{x-9}:\dfrac{9-x+x-4\sqrt{x}+4+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{3}{\sqrt{x}+3}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{x-4\sqrt{x}+4}\)
\(=\dfrac{3}{\sqrt{x}-2}\)
\(1,ĐKXĐ:x\ge0;x\ne4\)
\(A=\left(1+\frac{2}{\sqrt{x}}\right)\left(\frac{\sqrt{x}-2+\sqrt{x}+2-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(1+\frac{2}{\sqrt{x}}\right)\left(\frac{2\sqrt{x}-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(1+\frac{2}{\sqrt{x}}\right)\left(\frac{2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(\frac{\sqrt{x}+2}{\sqrt{x}}\right)\left(\frac{2}{\sqrt{x}+2}\right)\)
\(A=\frac{2}{\sqrt{x}}\)
\(2,A>\frac{1}{2}\)
\(\Leftrightarrow\frac{2}{\sqrt{x}}>\frac{1}{2}\)
\(\Leftrightarrow\frac{2}{\sqrt{x}}-\frac{1}{2}>0\)
\(\Leftrightarrow\frac{4}{2\sqrt{x}}-\frac{\sqrt{x}}{2\sqrt{x}}>0\)
\(\Leftrightarrow\frac{4-\sqrt{x}}{2\sqrt{x}}>0\)
Do \(\sqrt{x}>0\Rightarrow2\sqrt{x}>0\)
\(\Rightarrow4-\sqrt{x}>0\)
\(\Leftrightarrow-\sqrt{x}>-4\)
\(\Leftrightarrow\sqrt{x}< 4\)
\(\Leftrightarrow x< 16\)
Kết hợp với ĐKXĐ thì \(0\le x< 16\)và \(x\ne4\)
\(3,A=-2\sqrt{x}+5\)
\(\Leftrightarrow\frac{2}{\sqrt{x}}=-2\sqrt{x}+5\)
\(\Leftrightarrow\sqrt{x}\left(-2\sqrt{x}+5\right)=2\)
\(\Leftrightarrow-2x+5\sqrt{x}-2=0\)
\(\Leftrightarrow-2x+2.5\sqrt{x}+2.5\sqrt{x}-2=0\)
\(\Leftrightarrow\left(-2x+2.5\sqrt{x}\right)+\left(2.5\sqrt{x}-2\right)=0\)
Đến đây thì mình chịu
Bạn tự giải nốt nhé
HỌC TỐT
\(A=\frac{\left(1+\sqrt{x}\right)^2-4\sqrt{x}}{\sqrt{x}-1}\) \(\left(x\ge0;x\ne1\right)\)
\(A=\frac{x+2\sqrt{x}+1-4\sqrt{x}}{\sqrt{x}-1}=\frac{x-2\sqrt{x}+1}{\sqrt{x}-1}=\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}=\sqrt{x}-1\)
và \(B=\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{2}}+\frac{2+\sqrt{2}}{\sqrt{x}+1}\)
\(B=\frac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\)
\(B=\sqrt{3}+2+\frac{1}{\sqrt{3}-\sqrt{2}}+\sqrt{2}\)
\(B=\sqrt{3}+\sqrt{2}+\frac{1}{\sqrt{3}-\sqrt{2}}+2\)
\(B=\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)+1}{\sqrt{3}-\sqrt{2}}+2\)
\(B=\frac{3-2+1}{\sqrt{3}-\sqrt{2}}+2\)
\(B=\frac{2}{\sqrt{3}-\sqrt{2}}+2\)
để A = B thì \(\sqrt{x}-1\)= \(\frac{2}{\sqrt{3}-\sqrt{2}}+2\)
\(\sqrt{x}=\frac{2}{\sqrt{3}-\sqrt{2}}+3\)
\(\sqrt{x}=\frac{2\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}+3\)
\(\sqrt{x}=2\sqrt{3}+2\sqrt{2}+3\)
tới bước này tui bí :(( mong các bạn giỏi khác giúp bạn :D
\(\frac{4\sqrt{x}}{\left(\sqrt{x}+1\right)^2}=\frac{1}{2}\)
\(\Rightarrow4\sqrt{x}.2=1\left(\sqrt{x}+1\right)^2\)
\(\Rightarrow8\sqrt{x}=x+2\sqrt{x}+1\)
\(\Rightarrow x-6\sqrt{x}+1=0\)
\(a=1;b=-6;c=1;b'=-3\)
\(\Delta'=\left(-3\right)^2-1.1=9-1=8>0\)
Phương trình có 2 nghiệp phân biệt
\(x_1=\frac{-b'+\sqrt{\Delta'}}{a}=\frac{-\left(-3\right)+\sqrt{8}}{1}=3+2\sqrt{2}\)
\(x_2=\frac{-b'-\sqrt{\Delta'}}{a}=\frac{-\left(-3\right)-\sqrt{8}}{1}=3-2\sqrt{2}\)