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1) Nhìn cái pt hết ham, nhưng bấm nghiệm đẹp v~`~
\(\left(\sqrt{2}+2\right)\left(x\sqrt{2}-1\right)=2x\sqrt{2}-\sqrt{2}\)
\(\Leftrightarrow\left(\sqrt{2}+2\right)\left(x\sqrt{2}-1\right)-2x\sqrt{2}+\sqrt{2}=0\)
\(\Leftrightarrow2x-\sqrt{2}+2x\sqrt{2}-2-2x\sqrt{2}+\sqrt{2}=0\)
\(\Leftrightarrow2x-2=0\Leftrightarrow2x=2\Rightarrow x=1\)
;))) tớ nhớ dạng RGBT căn bậc 3 lớp 9 nhì :)))????
\(\left(\frac{2x+1}{\sqrt{x^3}-1}-\frac{\sqrt{x}}{x+\sqrt{x+1}}\right).\left(\frac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\right)\)
\(=\frac{2x+1-\sqrt{x}\left(\sqrt{x-1}\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left[\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{1+\sqrt{x}}-\sqrt{x}\right]\)
\(=\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x+1}\right)}.\left(1-2\sqrt{x}+x\right)\)
\(=\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\left(\sqrt{x}-1\right)^2\)
\(=\sqrt{x}-1\)
ĐKXĐ:...
\(\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{x+1}{3x}-x-1\right)\right]:\frac{x-1}{x}=\left[\frac{2}{3x}-\frac{2}{x+1}\left(\frac{-3x^2-2x+1}{3x}\right)\right]:\frac{x-1}{x}\)
\(=\left[\frac{2}{3x}-\frac{2\left(x+1\right)\left(1-3x\right)}{3x\left(x+1\right)}\right].\frac{x}{x-1}=\left(\frac{2}{3x}-\frac{2\left(1-3x\right)}{3x}\right).\left(\frac{x}{x-1}\right)\)
\(=\left(\frac{2-2+6x}{3x}\right)\left(\frac{x}{x-1}\right)=\frac{2x}{x-1}\)
đk: \(\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)
Ta có:
\(P=\left(\frac{1}{1-\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\div\left(\frac{2x+\sqrt{x}-1}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right)\)
\(P=\frac{\sqrt{x}-1+\sqrt{x}}{\left(1-\sqrt{x}\right)\sqrt{x}}\div\frac{\left(2x+\sqrt{x}-1\right)\left(x-\sqrt{x}+1\right)+\left(2x+\sqrt{x}-1\right)\left(\sqrt{x}-x\right)}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}\)
\(P=\frac{2\sqrt{x}-1}{\left(1-\sqrt{x}\right)\sqrt{x}}\cdot\frac{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}{2x+\sqrt{x}-1}\)
\(P=\frac{\left(2\sqrt{x}-1\right)\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}{\left(2\sqrt{x}-1\right)\left(1+\sqrt{x}\right)\sqrt{x}}\)
\(P=\frac{x-\sqrt{x}+1}{\sqrt{x}}=\frac{x\sqrt{x}-x+\sqrt{x}}{x}\)
a: \(P=x-\sqrt{x}-2\sqrt{x}-1+2\sqrt{x}+2=x-\sqrt{x}+1\)
b: \(P=\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\forall x\)
Dấu '=' xảy ra khi x=1/4